a 

to 

00 


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>- 


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o  rl 


IN 

»  Henry  Senger 


"**% 


^ 
n 


PAGES    OF    TABLES 

FROM 

RAYMOND'S  PLANE  SURVEYING 


Copyright,  1896,  by  AMERICAN  BOOK  COMPANY 


TV? 

3 


IN  MEMORIAM 

\i         '    "        r\ 


TABLES. 

V.   TABLES. 
TABLE   I. 


361 


CORRECTION  TO  ONE  HUNDRED  UNITS  MEASUR^  ALOF&  THE!,;  '\1 
SLOPES  GIVEN. 


UNITS  RISE  IN  100. 

CORRESPONDING 
VERTICAL  ANGLE. 

CORRECTION. 

1.02 

o°35' 

0.005 

2.01 

i°  09' 

O.O2O 

3-03 

i°  44' 

0.046 

4.02 

2°    1  8' 

0.081 

5.01 

2°    52' 

0.125 

6.00 

3°  26' 

0.179 

7.00 

4°  oo' 

0.244 

8.02 

4°  35' 

0.320 

9.01 

5°  09' 

0.404 

10.01 

5°  43' 

0.497 

20.01 

11°  19' 

1.617 

30.00 

1  6°  42' 

4.218 

40.00 

21°  48 

7.151 

50.00 

26°  34' 

10.559 

TABLE  II.i 

CORRECTION  COEFFICIENT  FOR  TEMPERATURE  AND  HYGROMETRIC 
CONDITIONS. 

This  correction  is  used  when  no  hygrometric  observations  have  been  made.  To  the 
difference  in  altitude  found  in  Table  III.  for  the  given  barometer  readings  is  added 
algebraically  the  product  of  that  difference  and  the  correction  below  given,  according 
to  the  formula,  Diff.  Alt.  =  (Diff.  by  Table  III.)  (1  +  c). 


SUM  O.  T.2 

CORR. 
COEFF.3 

SUM  O.  T. 

CORR. 

COEFF. 

SUM  0.  T. 

CORR. 
COEFF. 

0° 

- 
0.1024 

70° 

0.0273 

140° 

0.0471 

10 

0.0915 

80 

0.0166 

150 

0.0575 

20 

0.0806 

90 

0.0058 

160 

0.0677 

30 

0.0698 

100 

0.0049 

170 

0.0779 

40 

0.0592 

no 

0.0156 

1  80 

0.0879 

50 

0.0486 

120 

0.0262 

60 

0.0380 

I30 

0.0368 

1  Computed  from  Tables  I.  and  IV.,  Appendix  10,  "  U.  S.  Coast  Survey  Report "  for  1881. 
J  Sum  of  Observed  Temperatures.  8  Correction  Coefficient. 


362 


APPENDIX. 


TABLE   III.1 


BAROMETRIC   ELEVATIONS. 

Giving  altitudes  above  arbitrary  sea  level  (barometer  reading  30  inches) 
for  various  barometer  readings  B. 

To  determine  difference  of  elevation  of  two  points  having  barometer 
readings  B  and  Bv  take  from  the  table  the  altitudes  corresponding  to  B 
and  Bv  and  correct  their  difference  by  Table  II.  The  corrected  difference 
is  the  quantity  required. 


B. 

A. 

DlFF. 
FOR    .01. 

B. 

A. 

DlFF. 
FOR   .01. 

B. 

A. 

DlFF. 
FOR    .01. 

Inch  en. 

Feet. 

Feet. 

Inches. 

Feet. 

Feet. 

Inches. 

Feet. 

Feet. 

II.  O 

27,336 

—  24.6 

14.0 

20,765 

-19-5 

17.0 

15,476 

—  l6.O 

II.  I 

27,090 

24.4 

14.1 

20,570 

19-3 

17.1 

!5»3'6 

IS-9 

II.  2 

26,846 

24.2 

14.2 

20,377 

19.1 

I7.2 

'5,  '57 

J     s 

15.8 

"•3 

11.4 

26,604 
26,364 

24.0 

23.8 

14-3 
14.4 

20,186 
i  #997 

18.9 
18.8 

17-3 
17.4 

14,999 
14,842 

'5-7 
15.6 

"•5 

26,126 

23.6 

14-5 

19,809 

18.6 

17-5 

14,686 

15.5 

H.6- 

25,890 

23-4 

I4.6 

19,623 

18.6 

I7.6 

H,53i 

'5-4 

11.7 

25,656 

23.2 

14.7 

19,437 

18.5 

17.7 

'4,377 

'5-4 

u.  8 

25,424 

23.0 

14.8 

19,252 

18.4 

I7.8 

14,223 

11.9 

25,194 

22.8 

14.9 

19,068 

18.2 

17.9 

14,070 

!=;.  2 

I2.O 

24,966 

22.6 

I5.0 

18,886 

18.1 

18.0 

13,918 

J 

15.1 

12.  1 

24,740 

22-4 

'5-1 

18,705 

18.0 

18.1 

'3,767 

IS.O 

12.2 

24,516 

22.2 

15.2 

18,525 

17.9 

18.2 

13,617 

D 

14.9 

12.3 

24,294 

22.1 

'5-3 

18,346 

/     .7 

17.8 

18.3 

13,468 

14.9 

12.4 

24,073 

21.9 

15-4 

18,168 

17.6 

18.4 

'3,3'9 

14.7 

I2.5 

23,854 

21.7 

15-5 

17,992 

17.  c 

18.5 

I3,i72 

14.7 

12.6 

23,637 

/ 

21.6 

15.6 

17,817 

/     J 

17.4 

18.6 

13,025 

14.6 

I2.7 

23,421 

21.4 

15-7 

17.643 

18.7 

12,879 

14.6 

12.8 

23,207 

21.2 

15.8 

17,470 

17.2 

18.8 

'2,733 

14.4 

12.9 

22,995 

21.  0 

15-9 

17,298 

17.1 

18.9 

12,589 

14.4 

13.0 

22,785 

2O.9 

16.0 

17,127 

16.9 

19.0 

'2,445 

'3-' 

22,576 

20.8 

16.1 

16,958 

16.9 

19.1 

12,302 

14.2 

13.2 

22,368 

20.  6 

1  6.2 

16,789 

16.8 

19.2 

12,160 

14.2 

13-4 

22,162 
21,958 

20.4 
20.  i 

16.3 

16.4 

16,621 

16.7 
16.6 

19-3 
16.4 

12,018 
11,877 

14.1 
14.0 

'3-5 

2I,757 

20.  o 

16.5 

16,288 

16.4 

19-5 

",737 

13.9 

13.6 
'3-7 

2',557 
21,358 

19.9 
19.8 

16.6 
16.7 

16,124 
15,961 

16.3 
16.3 

19.6 
19.7 

",598 
",459 

O    s 

'3-9 
13.8 

13.8 

21,160 

-7     ** 

19.8 

16.8 

15,798 

*  w*  3 

16.2 

19.8 

11,321 

vJ 

17.7 

13-9 

20,962 

—  19.7 

16.9 

15,636 

—  16.0 

19.9 

11,184 

•J       1 

—  17.7 

14.0 

20,765 

7      / 

17.0 

15,476 

20.  o 

11,047 

o    / 

1  Taken  from  Appendix  10,  "  U.  S.  Coast  and  Geodetic  Survey  Report "  for  1881, 


TABLES. 


363 


TABLE   III.    (continued). 


B. 

A. 

DlFF. 
FOR   .01. 

B. 

A. 

DlFF. 
FOR   .01. 

B. 

A. 

DJFF. 

FOR   .01. 

Inches. 

Feet. 

Feet. 

Inches. 

Feet. 

Feet. 

Inches. 

Feet. 

Feet. 

20.0 

11,047 

-13.6 

23-7 

6,423 

—  u-5 

27.4 

2,470 

—   0.9 

2O.  I 
20.  2 
20.3 

10,911 
10,776 
10,642 

*  J"  v 

13-5 
13-4 

23-8 

23-9 
24.0 

6,308 
6,194 
6,080 

11.4 
11.4 

27.5 
27.6 
27.7 

2,371 
2,272 

2,173 

y.y 

9.9 

9-9 

Q  8 

20.4 

10,508 

13-3 

24.1 

5,967 

11.3 

27.8 

2,075 

y.  u 
9.8 

20.5 
20.  6 

io,375 
10,242 

13-3 

13.2 

24.2 
24-3 

5,854 
5,741 

"•3 

II.  2 

27.9 
28.0 

'.977 

,880 

9-7 
9.7 

20.7 

10,110 

o 

24.4 

5,629 

II.  I 

28.1 

,783 

9.7 

20.8 

9,979 

13  I 

24-5 

5.518 

I  I.I 

28.2 

,686 

•  / 
9.7 

20.9 

9,848 

13.0 

24.6 

5,407 

II.  I 

28.3 

,589 

y  / 

9.6 

21.0 
21.  1 

9,718 
9,589 

12.9 

12.9 

24.7 
24.8 

5,296 
5,186 

II.  O 
IO.9 

28.4 
28.5 

,493 
,397 

9.6 
g.c 

21.2 
21.3 

9,460 
9-332 

12.8 
12.8 

24.9 
25.0 

5,077* 
4,968 

IO.9 
IO.9 

28.6 
28.7 

,302 
,207 

-7     J 

9-5 
9.  c 

21.4 

9,204 

12.7 

25-1 

4,859 

10.8 

28.8 

,112 

s    D 

9.4 

21.5 

9,077 

12.6 

25.2 

4,751 

10.8 

28.9 

,018 

9.4 

21.6 

8,951 

12.6 

25-3 

4,643 

10.8 

29.0 

924 

9.4 

21.7 
21.8 

8,825 
8,700 

12.5 
12.5 

25-4 
25-5 

4,535 
4,428 

10.7 
10.7 

29.1 
29.2 

830 
736 

9.4 
9-3 

21.9 

8,575 

12.4 

25.6 

4,321 

10.6 

29-3 

643 

9-3 

22.0 

8,451 

12.4 

25-7 

4,215 

10.6 

294 

550 

9.2 

22.1 

8,327 

12.3 

25.8 

4,109 

10.1; 

•29-5 

458 

9.2 

22.2 

8,204 

12.2 

25-9 

4,004 

J 

IO.  C 

29.6 

366 

9.2 

22.3 

8,082 

12.2 

26.0 

3,899 

IV.  ^ 

10.1; 

29.7 

274 

•y     m 

Q.2 

22.4 

7,960 

12.2 

26.1 

3,794 

••  v   J 

10.4 

29.8 

182 

3r 

9.1 

22.5 

7,838 

12.  1 

26.2 

3,690 

10.4 

29.9 

91 

9.1 

22.6 

7,717 

12.0 

26.3 

3,586 

*v.*f- 
IO.3 

30.0 

oo 

9.1 

22.7 

7,597 

12.  0 

26.4 

3,483 

IO.T 

30.1 

-91 

Q.O 

22.8 

7,477 

II.9 

26.5 

3,38o 

AW.  ^ 

IO-3 

30.2 

181 

^/•^ 
9-O 

22.9 

7,358 

II.9 

26.6 

3,277 

IO.2 

30.3 

271 

9.0 

23.0 

7,239 

ii.  8 

26.7 

3,175 

10.2 

3°-4 

361 

9-0 

23.1 

7,121 

ii.  7 

26.8 

3,073 

IO.  I 

30.5 

45  l 

8.9 

23.2 

7,004 

/ 

II.  7 

26.9 

2,972 

IO.  I 

30.6 

540 

8.9 

23-3 

6,887 

/ 

II.7 

27.0 

2,871 

IO.  I 

3°-7 

629 

<7 

8.8 

23-4 

6,770 

/ 

ii.  6 

27.1 

2,770 

IO.O 

30.8 

717 

8.8 

23-5 

6,654 

1  1.  6 

27.2 

2,670 

IO.O 

30-9 

805 

-8.8 

23-6 

6,538 

—  II.  C 

27-3 

2,570 

—  IO.O 

31.0 

-893 

23-7 

6,423 

J 

27.4 

2,470 

\\ 


364 

u'* 


APPENDIX. 


TABLE  IV. 

POLAR  DISTANCE  OF  POLARIS.     For  January  1  of  years  named. 


1894 

1897 

1900 

1903 

1906 

1909 

1912 

1915 

1918 

1921 

1°  1543' 

1°  14.50' 

1°  13.55' 

1°  12.62' 

i°  11.68' 

i°  10.75' 

i°  09.82' 

i°  08.88' 

i°  07.97' 

i°  07.03' 

sin  polar  distance 

Sin  of  azimuth  at  elongation  = —. — : 

cosine  latitude 

Latitude  =  altitude  of  Polaris  at  culmination  ±  polar  distance  — refraction  correc- 
tion given  below. 


LATITUDE. 

CORRECTION,  MINUTES. 

LATITUDE. 

CORRECTION,  MINUTES. 

20° 

30 
40 

2.60 
l.65 
I.I3 

50° 
60 

0.80 
0-55 

TABLE   V.1 

AMOUNT  AND  VARIATION  OF  THE  MAGNETIC  NEEDLE  FROM  ITS 
MEAN  DAILY  POSITION. 

The  letters  E  and  W  indicate  which  side  of  the  mean  position  the  needle  points. 


LOCAL  MEAN  TIME  ;  MORNING  HOURS. 


6h 

7h 

8h 

9h 

10* 

nh 

I2h 

December,  January,  February  : 
Latitude  37°  to  49°    

/ 

o  7  E 

r 
i  i  E 

l 
i  o  F 

l 

2  2  E 

/ 

T   C   F 

/ 
n  T  W 

1 
T  8  W 

Latitude  25°  to  37°    ...... 

o  i  W 

o  i  E 

i  o  E 

2  O  E 

1.5  XL, 
2  2  F 

T    T    F 

n  e  \V 

March,  April,  May  : 
Latitude  37°  to  49°    

26E 

Q  8  E 

A  A  F 

•a  c  F 

T  f\  F 

o  8  \V 

Latitude  25°  to  37°    .... 

i  6  E 

28  E 

0    0    F 

oo  ^ 
2  6  E 

T   T    F 

n  f\  \V 

T  n  "W 

June,  July,  August  : 
Latitude  37°  to  49°    
Latitude  25°  to  37°    .... 

4.0  E 

2  A   E 

5-6  E 
4  o  E 

DO  -^ 

5-7  E 

A  2  F 

4-5  E 

2  O  F 

1.7  E 
r>  c  F 

1.6  E 

T   f\  W 

4.1  VV 

r>  8  W 

September,  October,  November: 
Latitude  37°  to  49°    .... 

i  8  E 

2  6  F 

4"s  « 

•3  T   F 

2  C.  E 

T  n  F 

T  e  F 

o  o  W 

Latitude  25°  to  37°    .    .     . 

2  I  E 

2  6  E 

2  I  E 

n  6  F 

1.5  & 
n  n  \V 

*\  W 

SEASON  AND  POSITION  IN  LATITUDE. 

LOCAL  MEAN  TIME;  AFTERNOON  HOURS. 

oh 

I* 

2* 

3h 

4h 

5h 

6* 

December,  January,  February  : 
Latitude  37°  to  49°    
Latitude  25°  to  37°    . 

/ 
1.8  W 
0.5  W 

3.8  W 
1.9  W 

4.1  W 

2.8  W 

3-3  W 

2.1  W 

/ 

2.9  W 
1.5  W 

4.8  W 
2.6  W 

5.6  W 
3.2  W 

4.0  W 
2.3  W 

/ 
2.8  W 
1.8  W 

4.6  W 
2.8  W 

5.6  W 
3.1  W 

3.4  W 
1.9  W 

1 
2.1  W 

1.6  W 

3-8  W 
2.4  W 

4.6  W 
2.4  W 

2.3  W 

1.2  W 

/ 
1.3  W 
i.oW 

2.5  W 
1.6  W 

3.0  W 
i.5  W 

1.2  W 

0.7  W 

/ 

0.7  W 
0.4  W 

1.4  W 

0.9  W 

1.4  W 
0.8  W 

0.6  W 
0.4  W 

/ 
0.2  W 

o.i  W 

0.7  W 
0.5  W 

0.6  W 
0.4  W 

o.i  W 

0.2  W 

March,  April,  May: 
Latitude  37°  to  49°    .... 

Latitude  25°  to  37°    . 

June,  July,  August  : 
Latitude  37°  to  49°    .... 

Latitude  2^°  to  37°    

September,  October,  November  : 
Latitude  37°  to  49°    .     .     .     .  •  .     . 

Latitude  25°  to  37°    

1  From  "  Manual  of  Instructions  "  issued  by  the  U.  S.  Land  Office  to  Surveyors  General. 


IS/ 


TABLES. 
TABLE   VI 


?> 

I.  VI 


365 


APPROXIMATE  LOCAL  MEAN  TIMES  (COUNTING  FROM  NOON  24  HOURS) 
OF  THE  ELONGATIONS  AND  CULMINATIONS  OF  POLARIS  IN  THE  YEAR 
1897  FOR  LATITUDE  40°  N. ;  LONGITUDE  6h  W.  FROM  GREENWICH. 


DATE. 

EAST 
ELONGATION. 

WEST                      UPPER 
ELONGATION.         CULMINATION. 

LOWER 
CULMINATION. 

h. 

rn. 

h. 

m. 

Jan.     i 

o 

38.2 

12 

27.8           6 

33-6 

18 

31-6 

15 

23 

39-0 

II 

32.5           5 

38.6 

!7 

36.3 

Feb.     i 

22 

31-8 

10 

25-4     i       4 

31.2 

16 

29.2 

'5 

21 

36.6 

9 

30-2           3 

35-9 

15 

33-9 

Mar.    i 

20 

41.4 

8 

34-9 

2 

40.7 

H 

38.7 

15 

19 

46.3 

7 

39-8 

I 

45-7 

13 

43-7 

Apr.     i 

18 

39-3 

6 

32-8 

O 

38-6 

12 

36.7 

May  l\ 

16 

—  —  i    -44-3 

5 

4 

37-8 
35-o 

23 
22 

39-7 
36.8 

—  U. 

10 

£1 

4L5 

15 

15 

46.6 

3 

40.1 

21 

41.9 

9 

43-9 

June    i 

H 

39-9 

2 

33-4 

2O 

35-3 

8 

37-3 

15 

13 

45-° 

I 

38.5 

19 

40.4 

7 

42.4 

July     i 

12 

42.4 

0 

35-9 

18 

37-8 

6 

39-8 

15 

II 

47-5 

23 

37-  * 

17 

42.9 

5 

44-9 

Aug.    i 

10 

41.0 

22 

30.6 

16 

36-4 

4 

38.4 

'5 

9 

46.! 

21 

35-7 

15 

41-5 

3 

43-5 

Sept.    i 

8 

39-5 

2O 

29.1 

H 

34-9 

2 

36.9 

15 

7 

44.6 

19 

34-2 

13 

40.0 

I 

42.0 

Oct.     i 

6 

41.8 

18 

3i-4 

12 

37-2 

0 

39-2 

15 

5 

46.8 

17 

36.4- 

II 

42.2 

23 

40-3 

Nov.     i 

4 

40.0 

16 

29.6 

10 

35-4 

22 

33-4 

15 

3 

44.8 

15 

34-4 

9 

40.2 

21 

38-2 

Dec.     i 

2 

41.8 

H 

3M 

8 

37-2 

2O 

35-2 

15 

1 

46-5 

!3 

36-1            7 

41.9 

19 

39-9 

To  refer  to  any  calendar  day  other  than  the  first  and  fifteenth  of  each  month, 
subtract  3.94™  for  every  day  between  it  and  the  preceding  tabular  day,  or  add 
3.94m  for  every  day  between  it  and  the  succeeding  tabular  day. 

To  refer  the  tabular  times  to  any  year  subsequent  to  the  year  1897,  add 
0.25m  (nearly)  for  every  additional  year  (after  1900,  0.2m). 

Also,  For  the  second  year  after  a  leap  year,  add,       0.9m. 

For  the  third  year  after  a  leap  year,  add,          1.7m. 
For  leap  year  before  March  1,  add,  2.6m. 

For  leap  year  on  and  after  March  1,  subtract,  1.2m. 

For  the  first  year  after  a  leap  year  the  table  is  correct,  except  for  the  regu- 
lar annual  change. 

To  refer  the  tabular  times  to  other  longitudes  than  six  hours,  add  when 
east,  and  subtract  when  west  of  six  hours,  0. 16m  for  each  hour. 

To  refer  to  any  other  than  the  tabular  latitude  between  the  limits  of  25°  and 
50°  north,  add  to  the  time  of  west  elongation  0.13m  for  every  degree  south  of 
latitude  40°,  and  subtract  from  the  time  of  west  elongation  0.18m  for  every  degree 
north  of  40°.  Reverse  these  signs  for  corrections  to  the  times  of  east  elongation. 
For  latitudes  as  high  as  60°,  diminish  the  times  of  west  elongation  and  increase 
the  times  of  east  elongation  by  0.23m  for  every  degree  north  of  latitude  40°. 

1  Computed  from  information  contained  in  the  "  Manual  of  Instructions  "  issued 
by  the  General  Land  Office.  The  information  was  furnished  by  the  U.  S.  Coast  and 
Geodetic  Survey. 


366 


APPENDIX. 

TABLE  VII.1 

REFRACTION  CORRECTIONS  TO  DECLINATION  OF  TEIE  SUN. 
The  hour  angle  is  the  time  either  side  of  noon. 


LATI- 
TUDE. 

HOUR 
ANGLE. 

DECLINATIONS. 

+  20° 

+i5D 

+  10° 

+5° 

0° 

-5° 

—  10° 

-15° 

—  2CP 

o   ' 

b. 

25  oo 

O 

o  05 

o  10 

0  '5 

0  21 

o  27 

o  33 

o  40 

o  48 

o  57 

2 

o  08 

o  14 

o  19 

o  25 

o  31 

o  38 

o  46 

o  54 

i  °5 

3 

0  12 

o  18 

o  24 

o  30 

o  37 

o  44 

o  53 

i  04 

i  18 

4 

o  23 

o  29 

o  35 

o  45 

o  53 

i  03 

i  16 

i  3i 

i  52 

5 

o  49 

o  59 

I  10 

i  24 

i  52 

2  07 

2  44 

3  46 

5  43 

27  30 

o 

o  08 

o  13 

o  18 

o  24 

o  30 

o  36 

o  44 

o  52 

I  02 

2 

O  II 

o  16 

0  22 

o  28 

o  34 

o  41 

o  49 

I  OO 

I  IO 

3 

o  17 

0  22 

o  28 

o  35 

o  42 

o  50 

I  00 

I  II 

I  26 

4 

o  28 

o  35 

o  42 

o  50 

I  OO 

I  II 

i  26 

1  43 

2  09 

5 

o  54 

I  05 

i  18 

i  34 

i  54 

2  24 

3  ii 

4  38 

8  15 

30  oo 

0 

O  IO 

0  15 

0  21 

o  27 

o  33 

o  40 

o  48 

o  57 

I  08 

2 

o  14 

o  19 

o  25 

o  31 

o  38 

o  46 

o  54 

i  05 

i  18 

3 

0  20 

o  26 

o  32 

o  39 

o  47 

0  55 

i  06 

i  19 

i  36 

4 

o  32 

o  39 

o  46 

o  52 

i  06 

i  19 

i  35 

i  57 

2  29 

5 

I  00 

I  10 

I  24 

i  52 

2  07 

2  44 

3  46 

5  43 

13  O6 

32  3° 

o 

o  13 

o  18 

o  24 

o  30 

o  36 

o  44 

o  52 

I  02 

I  H 

2 

o  17 

0  22 

o  28 

o  35 

o  42 

o  50 

I  00 

III 

I  26 

3 

o  23 

o  29 

o  35 

o  43 

o  5i 

I  01 

I  13 

I  28 

i  47 

4 

o  35 

o  43 

o  5i 

I  01 

I  13 

I  27 

I  46 

2  I3 

2  54 

5 

i  03 

i  '5 

1  31 

i  53 

2  2O 

3  °5 

4  25 

7  36 

— 

35  °° 

o 

0  15 

O  21 

o  27 

o  33 

o  40 

o  48 

o  57 

i  08 

I  21 

2 

0  20 

o  25 

o  32 

o  38 

o  46 

0  55 

i  °5 

i  18 

i  35 

3 

o  26 

o  33 

o  39 

o  47 

o  56 

i  07 

I  21 

i  38 

2  OO 

4 

o  39 

o  47 

o  56 

i  07 

I  20 

i  36 

i  59 

2  32 

3  25 

5 

i  07 

I  20 

i  38 

2  OO 

2  34 

3  29 

5  H 

10  16 

1  Computed  from  formula 


C=57"cot 


in  which  6  is  the  declination,  plus  when  north,  and  minus  when  south;  and  N  an 
auxiliary  angle  found  by 

tan  N=  cot  <J>  cos  t, 

in  which  <f>  is  the  latitude  of  the  place,  and  t  the  angle  between  the  meridian  of  the 
place  and  the  meridian  through  the  sun  at  the  given  time,  — called  the  "  hour  angle." 
The  formulae  are  from  Chauvenet's  "  Spherical  and  Practical  Astronomy,"  vol.  I., 
p.  171.  The  table  was  computed  by  Mr.  Edward  W.  Arms,  C.E.,  for  Messrs.  W.  & 
L.  E.  Gurley,  of  Troy,  N.Y.,  and  is  here  used  by  their  permission. 


TABLES. 


367 


TABLE   VII.    (continued). 


LATI- 
TUDE. 

HOUR 
ANGLE. 

DECLINATIONS. 

+20> 

-MS0 

+  I0c 

+5° 

00 

-5° 

—  10° 

-15° 

—  203 

o   ' 

h. 

,   .. 

37  3° 

0 

o  18 

o  24 

o  30 

o  36 

o  44 

o  52 

i  02 

i  14 

I  29 

2 

O  22 

o  28 

o  35 

o  42 

o  50 

I  00 

I  12 

i  26 

i  45 

3 

o  29 

o  36 

o  43 

o  52 

i  02 

I  14 

I  29 

i  49 

2  16 

4 

o  43 

0  51 

I  OI 

I  13 

i  27 

i  49 

2  I4 

2  54 

4  05 

5 

I  II 

i  26 

i  44 

2  10 

2  49 

3  55 

6  15 

H  58 

— 

40  oo 

0 

0  21 

o  27 

o  33 

o  40 

o  48 

o  57 

i  08 

I  21 

i  03 

2 

o  25 

o  32 

o  39 

o  46 

o  52 

i  06 

i  19 

i  35 

i  57 

3 

0  33 

o  40 

o  48 

0  57 

I  08 

I  21 

1  38 

2  O2 

2  36 

4 

o  47 

o  55 

i  06 

i  19 

1  36 

I  58 

2  30 

3  21 

4  59 

5 

i  15 

1  51 

2  2O 

3  05 

4  25 

7  34 

25  18 

— 

42  3° 

0 

o  24 

o  30 

o  36 

o  44 

o  52 

i  02 

i  14 

i  29 

i  49 

2 

o  28 

o  35 

o  39 

o  50 

I  00 

I  12 

i  26 

1  45 

2  II 

3 

o  36 

o  43 

o  52 

I  02 

I  13 

I  29 

i  49 

2  17 

2  59 

4 

o  50 

I  OO 

i  ii 

I  26 

i  44 

2  IO 

2  49 

3  55 

6  16 

5 

i  16 

1  36 

i  58 

2  30 

3  22 

C  OO 

9  24 

— 

45  °° 

0 

o  27 

o  33 

o  40 

0  48 

o  57 

I  08 

I  21 

i  39 

2  02 

2 

o  32 

o  39 

o  46 

o  52 

i  06 

I  19 

i  35 

i  57 

2  29 

3 

o  40 

o  47 

o  56 

I  07 

I  21 

1  38 

2  00 

2  34 

3  29 

4 

o  54 

i  04 

I  16 

i  33 

i  54 

2  24 

3  ii 

438 

8  15 

5 

i  23 

i  41 

2  05 

2  41 

3  40 

5  40 

12  02 

— 

— 

47  30 

o 

o  30 

o  36 

o  44 

o  52 

I  02 

i  14 

I  29 

i  49 

2  18 

2 

o  35 

o  42 

o  50 

I  OO 

I  12 

i  26 

1  45 

2  01 

2  51 

3 

o  43 

0  51 

I  01 

I  13 

I  28 

i  47 

2  15 

256 

408 

4 

o  56 

i  09 

I  23 

I  40 

2  05 

2  40 

3  39 

5  37 

ii  18 

5 

i  27 

i  46 

2  12 

2  52 

4  oi 

6  30 

16  19 

— 

50  oo 

0 

o  33 

o  40 

o  48 

o  57 

I  08 

I  21 

i  39 

2  O2 

236 

2 

o  38 

o  46 

o  55 

i  06 

i  18 

1  35 

i  57 

2  28 

3  19 

3 

o  47 

o  56 

i  06 

i  19 

i  36 

2  29 

2  31 

3  23 

5  02 

4 

I  02 

I  14 

i  29 

i  48 

2  16 

258 

4  18 

6  59 

19  47 

5 

I  30 

i  51 

2  19 

3  °4 

4  22 

7  28 

24  10 

— 

— 

52  3° 

0 

o  36 

o  44 

o  52 

I  02 

I  14 

i  29 

i  49 

2  18 

3  05 

2 

o  43 

o  50 

o  59 

I  II 

I  26 

i  42 

2  23 

2  49 

3  55 

3 

o  50 

I  00 

i  ii 

I  26 

1  45 

2  II 

2  51 

2  58 

6  22 

4 

1  °5 

i  18 

i  35 

2  10 

2  28 

3  19 

4  53 

842 

— 

5 

1  34 

i  56 

2  27 

3  16 

4  47 

852 

— 

— 

55  °° 

o 

o  40 

o  48 

0  57 

i  08 

I  21 

i  39 

2  02 

2  36 

3  33 

2 

3 

0  46 

o  55 

fli 

i  05 
i  19 

i  18 

i  35 

!3 

i  56 

2  30 

2  30 

3  21 

3  J5 

4  58 

4  47 
9  19 

4 

I  IO 

I  23 

i  42 

2  06 

2  43 

3  44 

5  49 

12  41 

— 

5 

i  37 

2  01 

2  34 

3  28 

5  15 

10  18 

— 

368 


APPENDIX. 


TABLE  VIII.1 
MAGNETIC  DECLINATION. 

Formulas  giving  approximately  the  magnetic  declination  at  the  places  named 
arid  for  any  time  within  the  limits  of  the  period  of  observation.  The  places  are  di- 
vided into  three  groups,  as  follows: 

GROUP  I. — Magnetic  stations  on  the  eastern  coast  of  the  United  States  and  in- 
clusive of  the  region  of  the  Appalachian  range,  with  some  additional  stations  in 
Newfoundland  and  other  foreign  localities. 

GROUP  II. — Magnetic  stations  mainly  in  the  central  part  of  the  United  States 
between  the  Appalachian  and  Rocky  Mountain  ranges,  with  additions  in  British 
North  America,  Canada,  the  West  Indies,  and  Central  America. 

GROUP  III. — Magnetic  stations  on  the  Pacific  coast  and  Rocky  Mountain  re- 
gion ;  also  in  Mexico  and  Alaska  and  in  some  foreign  countries. 

D  stands  for  declination,  +  indicating  west,  and  —  east  declination ;  m  stands 
for  t  —  1850.0  or  for  the  difference  in  time,  expressed  in  years  and  fraction  of  a  year, 
for  any  time  t  and  the  middle  of  the  century ;  a  *  indicates  uncertainty. 


6 
fc 

NAME  OF  STATION 
AND  STATE. 

LATI- 
TUDE. 

WEST 
LONGI- 
TUDE. 

THE  MAGNETIC  DECLINATION 
EXPRESSED  AS  A  FUNCTION  OF  TlME. 

GROUP  I. 

0       ' 

0        ' 

0 

0                                                              0 

i 

Saint    Johns,    New- 

47 34-4 

5241.9 

D=  +  21.94  + 

8.89  sin(i.o5  7/1  +  63.4)* 

foundland. 

2 

Quebec,  Canada. 

46  48.4 

71  H-5 

D=  +  i4.66  + 

3.035111(1.4    m+  4.6) 

+ 

0.61  sin  (4.0    TO  +  0.3) 

3 

Charlottetown,P.E.I. 

4614 

6327 

D=  +  i5-95  + 

7-78sin(i.2    7^  +  49.8) 

4 

Montreal,  Canada. 

45  30-5 

73  34-6 

D=  +  u.88  + 

4.i7sin(i.5    m—  18.5) 

+ 

0.363111(4.9    TO+I9) 

5 

Eastport,  Me. 

4454-4 

66  59.2 

D=  +  i5.i8  + 

3.79sm(i.25TO  +  3i.i)* 

6 

Bangor,  Me. 

4448.2 

68  46.9 

D=  +  i3.86+ 

3.55  sin(i.3o  TO  +  8.6) 

7 

Halifax,  Nova  Scotia. 

44  39-6 

6335-3 

D=  +  i6.i8  + 

4.53sin(i.o    7/1+46.1)* 

8 

Burlington,  Vt. 

4428.5 

73  12.0 

D=  +  10.81  + 

3.65  sin  (i.  30771  —  20.5) 

+ 

o.i8sin(7.o    771+132) 

9  Hanover,  N.  H. 

4342.3 

7217.1 

D=+  9.80  + 

4.o2sin(i.4   771  —  14.1)* 

ro|  Portland,  Me. 

43  38.8 

70  1  6.6 

D=  +  11.40  + 

3.28  sin(i.3o  TO+  2.7) 

ii  Rutland,  Vt. 

43  36-5 

7255-5 

D=  +  10.03  + 

3.82sin(i.5    791-24.3) 

1  2  Portsmouth,  N.  H. 

43  04-3 

7042.5 

D=  +  io.7i  + 

3.36  sin  (i.  44  m-   7.4) 

1  3  Chesterfield,  N.  H. 

4253-5 

7224 

D=+  9.60+ 

3.84  sin  (1.35  m—  1  6.1)* 

14  Xewburyport,  Mass.  14248.9 

7049.2 

D=  +  10.07  + 

3.02  sin  (  i.  35  m—   i.o) 

15  Williamstown,  Mass. 
16  Albany,  N.  Y. 

4242.8 
42  39-2 

73  13-4 
7345-8 

D  =  +   8.84+ 
D=+  8.17  + 

3.i3sin(i.4   771—14.0)* 
3.02  sin  (1.44  m—  8.3) 

17  Salem,  Mass. 

423^9 

7052.5 

D=  +  9.98  + 

3.85  sin  (i.  4    TO-  5.1)* 

18  Oxford,  N.  Y. 

42  26.5 

75  40.5 

D=+  6.19  + 

3.24  sin(i.35  m—  18.9) 

1  9,  Cambridge,  Mass. 

42  22.9 

7107.7 

D=+  9.54  + 

2.69  8111(1.30  TO+  7.0) 

o.i8sin(3.2    7/1  +  44) 

20  Boston,  Mass. 

4221.5 

71  °3-9 

D=+  9.48  + 

2.94  sin  (i.  3    TO+  3.7) 

21  Provincetown,  Mass. 

4203.1 

7011.3 

D=+  9.67  + 

3.o4sin(i-3    TO+II.O)* 

22  Providence,  R.  I. 

41  50.2 

71  23.8 

n=+  9.10+ 

2.99  sin  (i.  45  TO-  3.4) 

+ 

0.26  sin  (    7    TO  +  84) 

23 

Hartford,  Conn. 

4i  45-9 

72  40.4 

])=+  8.06+ 

2.90  sin(i.25  7/1  —  26.4) 

24!New  Haven,  Conn. 

41  18.5 

7255-7 

D=+   7.78  + 

3.11  sin(i.4ow  —  22.1) 

25!  Nan  tucket,  Mass. 

41  17.0 

70  06.0 

D=+  8.61  + 

2.83  sin(i.  35  TO+  19.7) 

26  Cold  Spring  Harbor, 

Long  Island,  N.  Y. 

4052 

7328 

D  =  +   7.19  + 

2?52sin(i.35  TO—  11.4) 

27 

New  York  City,  N.  Y. 

4042.7 

7400.4 

D=+   7.04+ 

2.77  sin(i.3o  m—  18.1) 

+ 

o.i4sin(6.3    7/1  +  64) 

1  From  Appendix  7,  "  U.  S.  Coast  and  Geodetic  Survey  Keport "  for  1888. 


TABLES. 


369 


6 

NAME  OF  STATION 

LATI- 

WEST 

THE  MAGNETIC  DECLINATION 

fc 

AND  STATE. 

TUDE. 

LONGI- 
TUDE. 

EXPRESSED  AS   A  FUNCTION   OF  TlME. 

O       ' 

0       • 

00                                                         0 

28 

Bethlehem,  Pa. 

40  36.4 

75  22.9 

D=  +  5.40+  3.13  sinCi.cc  711-38.3) 

2<> 

Huntingdon,  Pa. 

4031 

7802         D=  +  3.76+   2.93  sin(i.48  774-35.2) 

30 

New  Brunswick,  N.J. 

40  29.9 

74  26.8 

L>=  +   5.11+   2.94  sin  (1.30  7>i+  4.2) 

31 

Jamesburg,  N.  J. 

40  21 

7427 

D=  +  6.03+   2.94  sin  (1.40771  —  22.4) 

32 

Harrisburg,  Pa. 

40  15.9 

76  52.9 

D=  +  2.93+   2.98  sin  (i.  50  77i+  0.2) 

53 

Hatboro,  Pa. 

40  12 

7507 

D  =  +  5.17+  3.16  sin  (1.54  771  —  16.7) 

+  o.22sin(4.i    774  +  157) 

34 

Philadelphia,  Pa. 

39  56.9 

7509.0 

D-+   5-36+  3-I7sin(I-5°ra-26.i) 

+  0.195^(4.0   771+146) 

35 

Chambersburg,  Pa. 

3955 

7740 

D=+  2.79+  3.10  sin(i.55  774-30.6) 

+  0.20  sin  (4.6   771+124) 

30 

Baltimore,  Md. 

39  17-8 

76  37.0 

D=  +  3.20+  2.57  sin(i.45  7)t-2i.  2) 

37 

Washington,  D.  C. 

38  53-3 

7700.6 

D=+  2.73+  2.57  sin  (1.45  774-21.6) 

+  o.i4sin(i2    774  +  27) 

38 
39 

Cape  Henlopen,  Del. 
Williamsburg,  Va. 

3846.7 
37  16.2 

75  °5-° 
76  42.4 

D=+  4.01+  3.22  sin  (i.  35  771-25.2) 
D=+  2.33+  2.56sin(i.5    774-38.1) 

40  Cape  Henry,  Va. 
41  iNewbern,  N.  C. 

3655-6 
35  °6 

7600.4     :Dm+  2.42+  2.25  sin(i.477?4  —  30.6) 
7702        |D=  +  0.63+   2.56  sin(i.45  m—  18.2)* 

42 

Milledgeville,  Ga. 

33  04.2 

8312       iD=—  3.10+  2.53  sin(i.4om—  61.9)* 

43 

Charleston,  S.  C. 

3246.6 

7955.8      D=—   1.82+   2.75  sin  (i.  40  m—  12.1)* 

44  Savannah,  Ga. 

32  04.9 

81  05.5 

D=—  2.13+   2.55  sin{  i.  40  7/1—40.5)* 

45  Paris,  France. 

48  50.2 

2  20.2E 

D=    +  6°.479  +   i6°.oo2  sin  (0.765  m 

+  1  1  8°  46'.5   +   [0.85   —  0.35  sin 

(0.6974)]    sin    [(4.04  +  0.005474 

+  .000035  w'2)n] 

46 

St.     George's,     Ber- 

muda 

3223 

6442 

D=+  6.95+0.0145  774  +  0.000567742* 

47 

R  io  de  Janeiro,  Brazil 

-2254.8 

4309.5 

D=+   2.19  +  9.91  sin(o.8o  774—  10.4)* 

GROUP  II. 

i  York  Factory,  Brit- 

ish North  America 

56  59-9 

92  26 

D  =  +   7.34  +  1  6.03  sin  (  i.  io  774  -97.9) 

2 

Fort  Albany,  British 

North  America. 

5222 

8238 

0=1  +  15.78+   6.95  sin  (1.20774  —  99.6)  * 

3 

f  Duluth,  Minn.,  and 
(Superior  City,  Wis. 

46  45-5 
46  39-9 

92  04.5  1 
92  04.2  / 

D=—   7.70+   2.41  sin(i.4   m  —  120.0)* 

4 

Sault     Ste.     Marie, 

Mich. 

46  29.9 

8420.1 

D=+   1.54+  2.70  sin  (i.  45  771-58.5) 

5 

Pierrepont      Manor, 

N.Y. 

4344-5 

76  03.0 

D=+  5.95+  3.78sin(i.4   774-22.2) 

6 

Toronto,  Canada. 

43  39-4 

79  23-5 

D=+   3.60+   2.82sin(i.4   774—44.7) 

+  0.09  sin  (9.3    774+136) 

+  0.08  sin  (19    771  +  247) 

7 

Grand  Haven,  Mich. 

43°5-2 

86  12.6 

D=—  4-95+  0.0380774  +  0.00120  7?42 

8 

Milwaukee,  Wis. 

43  02.5 

87  54-2 

D=—  4.12+   3.60  sin  (1.45  m  —  64.5)* 

9 

Buffalo,  N.  Y. 

4252.8 

78  53-5 

D=+  3.66+  3.478^(1.4   774-27.8) 

10 

Detroit,  Mich. 

42  2O.O 

83  03.0 

D=—  0.97+   2.2isin(i.5    774  —  15.3) 

ii 

Ypsilanti,  Mich. 

42  H 

8338 

D=—   1.20+  3.40  sin  (i.  40  m—  4.1) 

12 

Erie,  Pa. 

42  07.8 

8005.4 

D  =  +  2.17+   2.69810(1.5    111-27.3) 

13  Chicago,  111. 

41  50.0 

87  36.8 

D=-  3.77+   2.48  sin(  i.  45  774  -62.5) 

14  Michigan  City,  Ind. 

41  434 

86  54.4 

D=—  3.23+   2.42  sin  (1.4   m  —  48.0) 

15  Cleveland,  O. 

41  30.4 

8141.5 

D=+  0.47+   2.39  sin  (1.30  m—  14.8) 

1  6  Omaha,  Neb. 

4i  15-7 

95  56-5 

D=-  9.30+  3.34  sin  (i.  30  774  -54.7) 

1  7  Beaver,  Pa. 

4044 

8020 

D=+   1.41+  2.72  sin(  i.  40  m  —  39.6) 

R'M'D  SURY.  — 24 


370 


APPENDIX. 


NAME  OF  STATION 

LATI- 

WEST 

THE  MAGNETIC  DECLINATION 

£ 

AND  STATE. 

TUDE. 

LONGI- 
TUDE. 

EXPRESSED  AS  A  FUNCTION   OF  TlME. 

18 

Pittsburg,  Pa. 

O       ' 

40  27.6 

O       ' 

8000.8 

O                        O                                                         O 

D=  +    1.85+  2.45  sin  (1.45  m  —  28.4) 

19 

Denver,  Col. 

3945-3 

104  59-5 

D  —  —  15.30+  o.oi  i  771+0.0005  w'2 

20 

Marietta,  O. 

3925 

81  28 

D=+  0.02+  2.89  sin  (1.4   771-40.5) 

21 

Athens,  0. 

39  19 

8202 

D=—   1.51+   2.63sin(i.4    771  —  24.7) 

22 

Cincinnati,  O. 

39  08.4 

8425.3 

D=-  2.59+   2.43  sin  (i.  42  771-37.9) 

23 

Saint  Louis,  Mo. 

38  38.0 

90  12.2 

D=r—   5.91+   3.00  sin  (1.40771  —  51.1)* 

24 

Nashville,  Tenn. 

36  08.9 

86  48.2 

D=-  3-57+  3-33  sin  (  I-  35  Wl~  68.5)* 

25 

Florence,  Ala. 

3447-2 

8741-5 

D=—  4.25+  2.33sin(i.3   771  —  52.8) 

26 

Mobile,  Ala. 

3041.4 

8802.5 

D=  —  4.38+   2.69801(1.45771  —  76.4) 

Pensacola,  Fla. 

30  20.  8 

87  18.3 

D=  —  4.40+  3.  1  6  sin  (1.4  771  —  59.4) 

27 

New  Orleans,  La. 

2957-2 

9003.9 

D=—  5.20+   2.98  sin  (1.40  77?.  —  69.8) 

28 

San  Antonio,  Tex. 

29  25.4 

98  29.3 

D-_   7.40+   2.88  sin  (i.  35  77i  -8  1.  8)* 

29 

Key  West,  Fla. 

24  33-5 

8  1  48.5 

I)=-  4.31+   2.86  sin(i.  30771-23.9) 

3° 

Havana,  Cuba. 

23  09.3 

8221.5 

D=-  4.25+  2.74  sin  (i.  25  7»  -23.3)* 

31 

Kingston,  Port  Royal, 

Jamaica. 

1755-9 

76  5°-6 

D=—  3.81+   2.39  sin  (i.  10  77i—  10.6) 

32 

Barbados,        Caribbee 

Islands. 

!305.7 

59  37-3 

T)=—   1.38+   2.  84  sin  (  1.  1  o  771+09.4) 

33 

Panama,  Colombia. 

857-i 

79  32-2 

D=  —  5.66+   2.22  sin(i.  10  771  —  27.8) 

GROUP  III. 

j 

Acapulco,  Mexico. 

16  50.5 

99  52-3 

D=—  4.48+  4.41  sin  (  i.  o   771  —  85.7)* 

2 

Vera  Cruz,  Mexico. 

19  11.9 

9608.8 

D=-   5.09+  4-22sin(i.2    771  —  63.4)* 

3 

City  of   Mexico,   Mex. 

19  26.0 

9911.6 

1)=—   5.34+   3.  28  sin  (  i.  o    771  —  87.9)* 

4 

San  Bias,  Mex. 

21  32.5 

105  18.4 

D=—   5.21+  4.265111(1.15771  —  96.5) 

5 

San      Lucas,       Lower 

Cal. 

2253-3 

109  54.7 

D=—  5.94+  3.68sin(i.2o  TO—  116.8)* 

6 

Magdalena  Bay,  Lower 

Cal. 

2438.4 

11208.9 

D=—  6.33+  4.17  sin(i.  15  m—  119.2)* 

-7 

Cerros   Island,    Lower 

/ 

Cal. 

2804 

115  12 

D=—   7.40+  4.61  sin  (1.05  77i—  107.0) 

8 

El  Paso,  Tex. 

3i  45-5 

1  06  27.0 

D=—  9.08+  3.40  sin  (1.3    771—108.4) 

9 

San  Diego,  Cal. 

3242.1 

"7  H-3 

D=  —  10.32  +   3.00  sin(i.io  m—  126.5) 

10 

Santa  Barbara,  Cal. 

34  24-2 

11943.0 

0^-11.52+  3.  32  sin(  1.  10  771—  123.1) 

ii 

Monterey,  Cal. 

3636-1 

121  53.6 

D=  —  13.25+  2.  83  sin  (i.  10  ?7i—  144.0) 

12 

San  Francisco,  Cal. 

37  47-5 

122  27.3 

D=-  13.94+  2.65  sin(  1.05  m-  135.5) 

»3 

Cape  Mendocino,  (y  al. 

40  26.3 

12424.3 

D—  —  15.25+  2.45  sin  (  1.  10  m—  128.0)* 

H 

Salt  Lake  City,  Utah. 

40  46.  i 

IH53-8 

D=  —  12.40  +  4.25sin(i.4   771—121.6)* 

IS 

Vancouver,  Wash. 

45  37-5 

12239.7 

D=-i7.93+  3.12  sin(i.35  m-  134.1)* 

1  6 

Walla  Walla,  Wash. 

4604 

Il8  22 

0^-17.80+  3.3osin(i.3    771-129.0)* 

r7 

Cape  Disappointment, 

Wash. 

46  16.7 

12402.8 

D=-  19.39+   2.54  sin(i.  25  m-  158.7) 

18 

Seattle,  Wash. 

47  35-9 

122  2O.O 

D=  —  19.19+  3.i4siii(i.4    771—136.1)* 

19 

Port  Townsend,  Wash. 

48  07.0 

122  44.9 

D=-  18.84+   3.00  sin  (i.  45m  -i  22.1) 

20 

Neah  Bay,  Wash. 

4821.8 

12438.0 

D=  —  19.83+   2.91  sin(i.4O  77i—  141.6) 

21 

Nootka,  Vancouver  Isl. 

49  35-5 

12637.5 

D—  —  21.25+   2.74  sin(i.  30  77i—  152.0)* 

22 

Captain's  and  Iliuliuk 

Harbors. 

53  52.6 

16631.5 

D=  —  18.01  +    i.82sin(i.3    771—69.6)* 

2  3 

Sitka,  Alaska. 

5702.9 

135  19-7 

0^-25.79+   3.30  sin(i.30  TO-  104.2) 

24 

St.  Paul,  Kadiak  Island. 

5748.0 

152  21.3 

D-  -22.21+   5.  i8sin(i.35  771-72.5) 

25 

Port  Mulgrave,  Alaska. 

59  33-7 

1  39  45  -9 

I>=  -24.03+   7.77  sin(  i.  30  771-  85.8) 

26 

Port  Etches,  Alaska. 

60  20.7 

14637.6 

D=-  23.71+   7.89  sin  (i.  35  7?i  -80.9) 

27 

Port  Clarence,  Alaska. 

65  16 

1  66  50 

D=-  18.98+   7.99sin(i.3    771-68.4)* 

28 

Chamisso  Isl.,  Alaska. 

6613 

161  49 

D=  -23.62+   7.648^(1.3   771-64.0)* 

29 

Petropaulovsk,  Siberia. 

53  oi 

2OI  17 

D--  3.35+   2.97sin(i.3    771+12.2) 

TABLES. 


371 


TABLE  IX. 


ANGULAR  CONVERGENCES  AND  DISTANCES  BETWEEN  MERIDIANS. 

1.  Angular  convergence  of  meridians  per  mile  of  easting  or  westing. 

2.  Distance  betweep  meridians  converging  by  one  minute. 


LATI- 
TUDE. 

ANGULAR  CON- 
VERGENCE PER 
MILE. 
MINUTES. 

DISTANCE  FOR 
CONVERGENCE 
OF  1'. 
FEET. 

LATI- 
TUDE. 

ANGULAR  CON- 
VERGENCE PER 
MILE. 
MINUTES. 

DISTANCE  FOR 
CONVERGENCE 

OFl'. 

FEET. 

0 

0 

I 

0.015 

348733 

31 

0.521 

10140 

2 

.030 

I743H 

32 

•542 

9751 

3 

.045 

116150 

33 

.563 

9382 

4 

.061 

87052 

34 

.585 

9034 

5 

.076 

69578 

35 

.607 

8703 

6 

.091 

57917 

36 

.630 

8387 

7 

.107 

49578 

37 

.653 

8087 

8 

.122 

43337 

38 

.677 

7801 

9 

•137 

38436 

39 

.702 

7527 

10 

•'53 

34525 

40 

.727 

7265 

ii 

.169 

31320 

4i 

•753 

7<>i3 

12 

.184 

28642 

42 

.780 

6770 

13 

.200 

26371 

43 

.808 

6537 

H 

.216 

24419 

44 

.836 

6313 

15 

.232 

22723 

45 

.866 

6097 

16 

.249 

21234 

46 

•897 

5888 

17 

.265 

19916 

47 

.929 

5686 

18 

.282 

18740 

48 

.962 

5491 

'9 

.299 

17685 

49 

.998 

5301 

20 

.316 

16731 

5° 

.032 

5118 

21 

•333 

15864 

5i 

.069 

4940 

22 

•350 

!5°73 

52 

.108 

4766 

23 

.368 

H348 

53 

.149 

4597 

24 

.386 

13680 

54 

.191 

4433 

25 

.404 

13062 

55 

.236 

4271 

26 

•423 

12488 

56 

.283 

4"5 

27 

.442 

"955 

57 

•333 

3962 

28 

.461 

"457 

58 

•385 

38i3 

29 

.480 

10990 

59 

.440 

3666 

30 

.500 

10552 

60 

•499 

3523 

372 


APPENDIX. 


TABLE   X.1 

LENGTH  OF  ONE  MINUTE  OF  LATITUDE  ANTD  ONE  MINUTE  OF  LON- 
GITUDE TO  THE  NEAREST  WHOLE  FOOT. 


LATI- 
TUDE. 

1'  LATITUDE. 
FEET. 

1'  LONGITUDE. 
FEET. 

LATI- 
TUDE. 

1'  LATITUDE. 
FEET. 

1'  LONGITUDE. 
FEET. 

o 

I 

6046 

6086 

o 

31 

6062 

5222 

2 

6046 

6083 

32 

6063 

5^7 

3 

6046 

6079 

33 

6064 

5110 

4 

6046 

6072 

34 

6065 

5052 

5 

6046 

6064 

35 

6066 

4992 

6 

6047 

6054 

36 

6067 

4930 

7 

6047 

6042 

37 

6068 

4867 

8 

6047 

6028 

38 

6069 

4803 

9 

6047 

6013 

39 

6070 

4737 

10 

6048 

5995 

40 

6071 

4670 

ii 

6048 

5976 

4i 

6072 

4601 

12 

6049 

5955 

42 

6074 

4531 

13 

6049 

5932 

43 

6075 

4459 

H 

6050 

5908 

44 

6076 

4386 

15 

6050 

5881 

45 

6077 

4312 

16 

6051 

5853 

46 

6078 

4236 

*7 

6051 

5823 

47 

6079 

4159 

18 

6052 

579i 

48 

6080 

4081 

19 

6052 

5758 

49 

6081 

4001 

20 

6053 

5722 

50 

6082 

3921 

21 

6054 

5685 

5i 

6083 

3839 

22 

6055 

5647 

52 

6084 

3756 

23 

6055 

5606 

53 

6085 

3671 

24 

6056 

5564 

54 

6086 

3586 

25 

6057 

5520 

55 

6087 

3499 

26 

6058 

5475 

56 

6088 

3412 

27 

6059 

5427 

57 

6089 

3323 

28 

6059 

5379 

58 

6090 

3234 

29 

6060 

5328 

59 

6091 

3H3 

30 

6061 

5276 

60 

6092 

305  ! 

1  Abbreviated  from  the  Smithsonian  Geographical  Tables. 


TABLES. 


373 


TABLE  XI. 
TRIGONOMETRIC  FUNCTIONS  AND  FORMULAS.     SOLUTION  OF  TRIANGLES. 


By  definition,  if  R  =  1, 

ED  —  sine  a. 
OD  =  cosine  a. 
DA  =  versed  sine  «. 
HF '  =  coversed  sine  a. 
BA  =  tangent  a. 
FC  =  cotangent «. 
OB  =  secant  «. 
OC  =  cosecant  «. 

If  R  is  other  than  1,  it  follows  from 
the  above  definitions  and  the  propor- 
tionality of  similar  figures,  that 

1.  ED  =  R  sin  a. 

2.  OD  =  Rcosa. 

3.  DA  =  R  versin  a. 

4.  HF  =  R  co versin  a. 


G        c 


5.  BA  =  R  tan  a. 

6.  FC  =  Rcota. 

7.  OB  =  R  sec  «. 

8.  OC  =  R  cosec  a. 


from  which  also  in  any  right  triangle  of  angles  «  and  (3,  if  o  be  the  side 
opposite  the  angle  a,  a  the  side  adjacent  thereto,  and  h  the  hypotenuse, 


9.      sin  a  =  -  =  cos  ft. 
h 

10.      cos  a  =  -  =  sin  ft. 
h 


11. 


Hence, 
17. 

18. 
19. 


12.      cot  a  =  -  =  tan  ft. 


sin  a     cos  /? 
a  =  h  cos  a  =  h  sin  /?. 


. 
cos  a     sin  /? 

0  =  a  tan  a  =  a  cot  ft. 

a  =  -?-  =  -?-. 
tan  a     cot  ft 


13.          sec  a  =  -  =  cosec  ft. 


14.  cosec  a  =  -  =  sec  B. 

o 

15.  vers  a  =     ~  rt  =  covers  ft. 

h 

16.  covers  a  =     ~  °  =  vers  /?. 


20. 


a  =  o  cot  a  =  o  tan  ft. 
a  a 


o  = 


cot «      tan 


(  h  =  a  sec  a  =  a  cosec 

21.  1  h     =       A 

sec  a     cosec  /3 
^  =  o  cosec  a  =  o  sec  y 

22.  ^     =      "ft      =     A 

cosec  a     sec  ft 


374 


APPENDIX. 


23.  o  =  VA2-a2 

24.  a  =  V^2  -  o2  =  V(ft  -f  o) (h  -  o). 


Oblique  triangles  may  be  solved  by  some  one  of  the  following  formulas  :       \* 

••-"'     LX  yJA^A,-  " 


GIVEN.  I       SOUGHT.  . 


FORMULAS. 


/E 


27.    A,B,a, 

28.   A,  a,  b, 

29.    C,  a,  6, 
30. 
81. 

32. 

33. 
34.   a,  6,  c, 

35. 
36.    A,B,Ct  a, 

C,  o,  c, 

5,  C,  c, 
i  (>4  4  5), 

^,B, 

c, 

Area, 
-4, 

Area, 
Area, 

« 

sin  yl 
r           a      ifri  (4    i    R^ 

sin  A 
"in  R      sm  ^4  -,      .0,       ieo°       ^  4  4^  R"» 

a 

c  ^     a    sin  C. 
sin  ^4 

J(^  +  -B)=90°-  JC» 
tan  ^  (^4      B)  —  a  ~~    tan  A  (^4  +  B) 

a  +  b 

'_•"    &^l(d+? 

sin  2  (^4  —  -B) 
Area  =  ^  a&  sin  C. 
If  s  =  J  (a  4  &  4  c), 

tan?  4       J0-&)0-<0 

A       2  Vs^  —  a)(s  -  6)(s  —  c) 

vt-is  yi 
&c 

Area  =  Vs(s  —  a)  (s  —  6)  (#  —  c)  . 
\rca  _  fl2  sin  5  sin  C 

2  sin  4 

\ 


TABLES.  375 

From  the  definitions  of  the  trigonometric  functions,  the  geometrical 
properties  of  right  triangles  and  in  some  cases  algebraic  transformations,  it 
may  be  shown  that  if  A  is  any  angle  and  B  any  other  angle, 

37.     sin2  A  +  cos2  A  =  1. 


38.  sin  A  =  — =  Vl  —  cos2  A  =  tan  A  cos  A 

cosec  A 

=  2  sin  |  A  cos  \A  =  vers  A  cot  \  A 
=  Vi  vers  2  A  =  V|(l  -cos  2  A). 

39.  cos  A  =  — —  =  VI  -  sin'2  A  =  cot  A  sin  A 

sec  A 

=  1  -vers  A  = 


=  cos2  \A-  sin2  i  .4  = 
40.     tan  A  =sinA         1 


cos  A      cot  ^4 


=  Vsec2.4  -1 


VI  -  cos2  4          sin  2  A 


cos2  A  cos  ^4  1  +  cos  2 

1  -  cos  2  ^4  _  vers  2 .4 
sin  2  A  sin  2  ^4 


=  cot  i  ^4  (sec  A  -1). 


41.     cot.4  =cos      =  __       =  Vcosec2 .4  -  1 
sm  A      tan  A 

sin  2  .4          sin  2  ^       1  +  cos  2 .4 


1  —  cos  2  A      vers  2  ^4         sin  2  A         sec  A  —1 

42.  vers  .4  =  1  -cos  A  =  sin  A  tan  $  ^4  =  2  sin2i  .4  =  cos  A  (sec  ^4  - 1) . 

43.  sin  (A  ±  J5)  =  sin  A  cos  5  ±  sin  B  cos  ^4 . 

44.  cos  (A  ±  B)  =  cos  A  cos  5  T  sin  ^4  sin  5. 


Az       -•-  i   *         'A  —  uua  ..-a         /vers 


46.      sin  2  ^4  =2  sin  .4  cos 


47. 


COS 


2 

48.  cos  2 ,4  =  2 cos2 .4  -I  =  cos2.4  -sin2y4  =  l- 

49.  tanM  =     **"  '*     =  cosec  .4  -  cot  A  =  1  ~  cos  A 

1  +  sec  .4  sin  A 

50.  tan  2 .4  =      2tan^ — . 

1  -tan2M 

51.  cot  |  4=  sin^  =l+™sA= 1_ 

vers  A          sin  A          cosec  ^4  —  cot  A 


376 


APPENDIX. 


52.   cot   2  A  = 


53.   vers  *  A  = 


cot2 .4  -1 
2  cot  ,4 
£  vers  ^4 


1  —  cos  A 


-  £  vers  J.      2  4-  V2(l  +  co 

54.  vers  2  ^4  =  2  sin2  A. 

55.  sin  ^4  +  sin  £  =  2  sin  \  (A  +  B)  cos  %(A  -  B). 

56.  sin  ^4  -  sin  B  =  2  cos  £  (.4  +  JB)  sin  £  (4  -  5) 

57.  cos  A  +  cos  £  =  2  cos  J  (4  +  B)  cos  J  (4  -  5) 

58.  cos   B  -  cos  4  =  2  sin  }  (4  +  B)  sin  J  (.4  -  £) 

59.  sin2  A  -  sin2  £  =  cos2!?  -  cos2  ,4  =  sin  (A  +  5 

60.  cos2  4  -  sin2  B  =  cos  (4  +  B)  cos  (.4  -  5). 


61. 


62.   tan  A  - 


cos  y4  cos  B 


cos  ^4  cos  x> 


sn 


-  B). 


TABLE  XII. 

LENGTHS  OF  CIRCULAR  ARCS  OF  RADIUS  1,  AND  VARIOUS 
CIRCULAR  MEASURES. 


No. 

DEGREES. 

MINUTES. 

SECONDS. 

No. 

DEGREES. 

MINUTES. 

SECONDS. 

i 

•0174533 

.0002909 

.0000048 

6 

.1047198 

.0017453 

.0000291 

2 

.0349066 

.0005818 

.0000097 

7 

.1221730 

.0020362 

.0000339 

3 

•0523599 

.0008727 

.0000145 

8 

.1396263 

.0023271 

.0000388 

4 

.0698132 

.0011636 

.0000194 

9 

.1570796 

.0026180 

.0000436 

5 

.0872665 

•0014544 

.0000242 

10 

-1  745329 

.0029089 

.0000485 

Degrees  in  arc  of  length  equal  to  radius,    57.°  295  780. 
Degrees  in  arc  of  length  equal  to  TT,  180.°  000  000. 

Circumference  =  2  TIT  =  360.°  000  000. 

Area  =  Trr2. 


'.  I  =  length  of  circular  arc 
d  —  number  of  degrees  in  same 
r  =  radius  of  same 
c  =  chord  of  same 
m  =  middle  ordinate 


180° 


r  -  L  .  18Q°. 
d       IT 


Area  of  sector  =  |  Ir. 

Area  of  sector  =  — —  Trr2. 
360 

Approximate  area  of  segment  =  f  cm. 


TABLES. 


377 


TABLE   XIII. 
LINEAR  TRANSFORMATIONS. 

1.    Gunter's  Chains  to  Feet. 


CHAINS. 

O.O 

O.OI 

.02 

.03 

.04 

•05 

.06 

.07 

.08 

.09 

0.0 

.66 

1.32 

I.98 

2.64 

3.30 

3.96 

4.62 

5.28 

5-94 

.1 

6.60 

7.26 

7.92 

8.58 

9.24 

9.90 

10.56 

11.22 

11.88 

12.54 

.2 

13.20 

13-86 

14.52 

I5.I8 

15.84 

16.50 

17.16 

17.82 

18.48 

19.14 

•3 

19.80 

20.46 

21.12 

21.78 

22.44 

23.10 

23.76 

24.42 

25.08 

25-74 

•4 

26.40 

27.06 

27.72 

28.38 

29.04 

29.70 

30-36 

31.02 

31-68 

32.34 

•5 

33-00 

33-66 

34-32 

34.98 

35.64 

36-30 

36.96 

37.62 

38.28 

38.94 

.6 

39.60 

40.26 

40.92 

41.58 

42.24 

42.90 

43-56 

44.22 

44.88 

45-54 

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46.20 

46.86 

47-52 

48.18 

48.84 

49.5° 

50.16 

50.82 

51.48 

52.14 

.8 

52.80 

53-46 

54.12 

54.78 

55-44 

56.10 

56.76 

57-42 

58.08 

58.74 

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59-40 

60.06 

60.72 

61.38 

62.04 

62.70 

63-36 

64.02 

64.68 

65-34 

0.0 

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3-0 

4.0 

5-0 

6.0 

7.0 

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66 

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198 

264 

330 

396 

462 

528 

594 

10.0 

660 

726 

792 

858 

924 

990 

1056 

1122 

1188 

1254 

20.0 

1320 

1386 

1452 

1518 

1584 

1650 

1716 

1782 

1848 

1914 

30.0 

1980 

2046 

2112 

2178 

2244 

2310 

2376 

2442 

2508 

2574 

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2706 

2772 

2838 

2904 

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3102 

3168 

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5082 

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80.0 

5280 

5346 

5412 

5478 

5544 

5610 

5676 

5742 

5808 

5874 

378 


APPENDIX. 


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TABLES. 


379 


3.    Feet  to  Meters. 


Vwf 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

iVEET. 

Meters. 

Meters. 

Meters. 

Meters. 

Meters. 

Meters. 

Meters. 

Meters. 

Meters. 

Meters. 

0 

O.OOO 

0.305 

0.610 

0.914 

I.2I9 

1.524 

1.829 

2.134 

| 
2.438 

2-743 

10 

3.048 

3-353 

3.658 

3.962 

4.267 

4-572 

4.877 

5.182 

5.486 

5-791 

20 

6.036 

6.401 

6.706 

7-010 

7-3I5 

7.620 

7.925 

8.229 

8-534 

8.839 

30 

9.144 

9-449 

9-753 

10.058 

10.363 

10.668 

10.972 

11.277 

11.582 

11.887 

40 

12.192 

12.496 

12.801 

13.106 

13.411 

13.716 

14.020 

H.325 

14.630 

H-935 

50 

I5-239 

15-544 

15.849 

16.154 

16.459 

16.763 

17.068 

17-373 

17.678 

17-983 

60 

18.287 

18.592  18.897 

19.202 

I9-507 

19.811 

20.116 

20.421 

20.726 

21.031 

70 

21-335 

2  1  .640 

21-945 

22.250 

22-555 

22.859 

23.164 

23.469 

23-774 

24.079 

80 

24.383 

24.688 

24.993 

25.298 

25.602 

25.907 

26.212 

26.517 

26.822 

27.126 

90 

27-43I 

27.736 

28.041 

28.346 

28.651 

28.955 

29.260 

29.565 

29.870 

3°-I74 

100 

30.479 

30.784 

31.089 

31-394 

31.698 

32.003 

32.308 

32.613 

32.918 

33-222 

4.   Meters  to  Feet. 


\f   T-T-T 

o 

I 

2 

3 

4 

5 

6 

7 

8 

9 

METEKS. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

0 

O.OO 

3.28 

6.56 

9.84 

I3-I2 

16.40 

19.69 

22.97 

26.25 

29-53 

10 

32-81 

36.09 

39-37 

42.65 

45-93 

49-21 

52.49 

55-78 

59.06 

62.34 

2O 

65.62 

68.90 

72.18 

7546 

78.74 

82.02 

85.30 

88.58 

91.87 

95-'5 

3° 

98.43 

101.71 

104.99 

108.27 

"1-55 

114.83 

118.11 

121.39 

124.67 

127.96 

40 

131.24 

I34-52 

i37-8o 

141.08 

144.36 

147.64 

150.92 

154.20 

157-48 

160.76 

50 

164.04 

167.33 

170.61 

173.89 

177.17 

180.45 

183.73 

187.01 

190.29 

193-57 

60 

196.85 

200.13 

203.42 

206.70 

209.98 

213.26 

216.54 

219.82 

223.10 

226.38 

70 

229.66 

232.94 

236.22 

239-5  * 

242.79 

246.07 

249-35 

252.63 

255-9I 

259.19 

80 

262.47 

265.75 

269.03 

272.31 

275.60 

278.88 

282.16 

285.44 

288.72 

292.00 

90 

295.28 

298-56 

391-84 

305.12 

308.40 

311.69 

3H.97 

318.25 

321.53 

324-81 

IOO 

328.09 

331-37 

334-65 

337-93 

341.21 

344-49 

347.78 

351.06 

354-34 

357-62 

i  statute  mile  =  1.6093  kilometers 
I  kilometer      =  0.6214  statute  miles 


"*.?, 

>«"' 

TABLE  XIV. 

DISTANCES  AND  DIFFERENCES  OF  ELEVATION.  CO 

al  angles.  The  values  for  other  readings  are  obtained  by  multiplying  the  quantities  under  o 
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382 


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II        II        II 

TABLES   XV,    XVI. 

COMMON   LOGARITHMS  OF   NUMBERS. 
LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


EDITED   BY  C.  W.   CROCKETT. 


3*3 


NOTE. 

THE  well-known  tables  of  Gauss,  Hoiiel,  Becker,  and 
Albrecht  have  been  taken  as  the  standards,  and  the  figures 
compared  with  the  more  extensive  tables,  the  doubtful  cases 
being  recomputed. 


384 


EXPLANATION    OF    THE    TABLES 

INTRODUCTORY. 

1.  When  we  have  a  number  with  six  or  more  decimal  places,  and  we 
wish  to  use  only  five  : 

(a)  If  the  sixth  and  following  figures  of  the  decimal  are  less  than 
5  in  the  sixth  place,  they  are  dropped;  thus,  0.46437  4999  is  called 
0.46437. 

(£)  If  the  sixth  and  following  figures  of  the  decimal  are  greater  than 
5  in  the  sixth  place,  the  fifth  place  is  increased  by  unity  and  the  sixth 
and  following  places  are  dropped;  thus,  0.46437  5001  is  called  0.46438. 

(c)  If  the  sixth  figure  of  the  decimal  is  5,  and  if  it  is  followed  only  by 
zeros,  make  the  fifth  figure  the  nearest  even  figure  ;  thus,  0.46437  500  is 
called  0.46438,  while  0.46438  500  is  also  called  0.46438.  The  number 
is  thus  increased  when  the  fifth  figure  is  odd,  and  decreased  when  it  is 
even,  the  two  operations  tending  to  neutralize  each  other  in  a  series  of 
computations,  and  hence  to  diminish  the  resultant  error. 

2.  Hence  any  number  obtained  according  to  Art.  i  may  be  in  error 
by  half  a  unit  in  the  fifth  decimal  place. 

3.  When  the  last  figure  of  a  number  in  these  tables  is  5,  the  number 
printed  is  too  large,  the  5  having  been  obtained  according  to  Art.  i  (b  \  ; 
if  the   5    is  without  the   minus   sign,  the  number  printed  is  too  small, 
the  figures  following  the  5  having  been  dropped  according  to  Art.  i  (<?). 

4.  The  marginal  tables  contain  the  products  of  the  numbers  at  the 
top  of  the  columns  by  i,  2,  3,  •••  9  tenths,  and  may  be  used  in  multiply- 
ing and  dividing  in  interpolation. 

(a)  To  multiply  38  by  .746  : 


38  x. 7=  =26.6 

38  X  .4  =  i5-2  ;  •'•  38  X  .04    =     1.52 
38  X  .6  =  22.8  ;  .-.  38  X  .006  =      .228 
.-.  38  x  .746  =  28.348 


3-8 
7.6 
11.4 
15.2 
19.0 

22.8 
26.6 

3°-4 
9     34-2 


In  multiplying  by  the  second  figure  (hundredths),  the  decimal  point 
in  the  table  is  moved  one  place  to  the  left ;  in  multiplying  by  the  third 
(thousandths),  two  to  the  left;  and  so  on. 


H'M'D  st  KV.  —  25 


(385) 


386  EXPLANATION   OF    THE   TABLES. 

(b)  To  divide  28  by  38  : 


Next  less,  26.6    ,  corresponding  to  .7                     l 

Remainder,      14  3 

Next  less,         i  1.4  corresponding  to  .03  f 

Remainder,         26  7 

Nearest,               2  6.6  corresponding  to  .007 


/.  Quotient,  .737 


9 


to  the  nearest  third  decimal  place.     The  decimal  point  is  moved  one 
place  to  the  right  in  each  remainder,  since  the  next  figure  in  the  quotient 
will  be  one  place  farther  to  the  right. 
To  divide  23  by  38  : 

Dividend,      23 

22.8         corresponding  to  .6 

2 

o.o      corresponding  to  .00 

2  o. 
Nearest,  i  9.0  corresponding  to  .005 

.-.  Quotient,  .605 

The  computer  should  use  the  marginal  tables  mentally. 


LOGARITHMS. 

5.  The  logarithm  of  a  number  is  the  exponent  of  the  power  to  which 
a  given  number  called  the  base  must    be  raised    to  produce  the   first 
number.     If  A  =  ea,  a  is  called  the  logarithm  of  the  number  A  to  the 
base  <?,  written  loge  A  =  a. 

6.  If  A  =  ea,  and  B  =  eb,  or  (omitting  subscripts)  log  A  =  a,  and 
log  B  =  b,  we  have 

Ax£  =  ea+b;    .-.  \og(A  x  B)  =  a  +  b  •   /.  \og(A  x^)  =log 

^)  -log  A- 


ia  n .—  i  _  i 

V  A      =  en   :     /.  \ogVA         —  —  a  :       .-.  log  v  A        —- 

n  n 


EXPLANATION    OF   THE    TABLES.  387 

7.  When  the  base  is  not  specified,  it  is  generally  understood  that 
logarithms  to  the  base  10,  or  common  logarithms,  are  meant.  In  this 
system,  since 

i  i 

o.ooi  =  —     -  =  — 5  =  io~',        log  o.oo i  =  —  7  ; 

1000         10' 

i  i 

O.OI      =  —          = r,=  IO    ",          1O2O.OI      =  —2; 

100  10- 


o.i       =—       = —  =  IO"1.        log  o.i      =—  i  : 

JO  10 

i.  10°,  log         i=      o; 

io.  =              io1,  log       10  =  4-1; 

100.  =             io2,  log     100  =  4-2: 

1000.  io3,  log  1000  =  4- 3- 

8.  The  logarithm  of  a  number  between  100  and  1000  will  be  a  num- 
ber between   2  and  3,  or  2  4-  M  where  ;;/  will  be  a  decimal  called  the 
mantissa,  the  integral  portion  of  the  logarithm  being  the  characteristic. 
The  mantissa  is  always  considered  positive;    thus  log 0.002  will  be  a 
number  between   —  2  and   —  3,  that  is,  either  —  3  4-  m  or  —  2  —  m', 
the  first  form  being  used.     We  write  log  0.002  =  3.30103,  the  negative 
sign  being  placed  over  the  characteristic  to  show  that  the  characteristic 
alone  is  negative. 

9.  Since 

log  (A  x  ion)  =  log  A  4-  log  io"  =  log  A  4-  ;/  log  io  =  \ogA  4-  n, 
and  log  (A  -=-  ion)  =  log  A  —  log  10"  =  log  A  —  n  log  io  =  log^4  —  n, 
we  have,  if  log  37.3  =  1.57171, 

Iog373-  =2.57171,  and  Iog3.73  =0.57171; 
Iog373°  =3-57I7I>  and  logo.373  =1.57171; 
Iog373°°  =  4-57I7I>  and  ^0.0373  =  2.57171. 

Hence  the  position  of  the  decimal  point  affects  the  characteristic  alone, 
the  mantissa  being  always  the  same  for  the  same  sequence  of  figures. 
For  this  reason  the  common  system  of  logarithms  is  used  in  practice. 

10.  The    characteristic   is    found    as  follows  :      M'hen  t/ie  number  is 
greater  t/iiin  i,  the  characteristic  is  positive,  and  is  one  less  than  the  num- 
ber of  digit*  to  the  left  of  the  decimal  point ;  when  the  number  is  less 
than  i,  the  characteristic  is  negative,  and  is  one  more  than  the  number 
of  zeros  between  the  decimal  point  and  the  first  significant  figure. 

11.  To  avoid  the  use  of  negative  characteristics  we  add  io  to  the 
characteristic  and  write  —  io  after  the  mantissa,  i.e.  adding  and  subtract- 
ing the  same  quantity,  io.     Thus  log  o. 2  =  1.30103  would   be  written 


388  EXPLANATION   OF   THE   TABLES. 

9.30103  —  10.  The  —  10  is  often  omitted  for  brevity  when  there  is  no 
danger  of  confusion,  but  its  existence  must  not  be  forgotten.  Such 
logarithms  are  called  augmented  logarithms. 

In  this  case  the  characteristic  of  the  logarithm  of  a  pure  decimal  is  9 
diminished  by  the  number  of  ciphers  to  the  left  of  the  first  significant 
figure.  Thus  the  characteristic  of  log  0.004  is  9  —  2,  or  7,  and  that  of 
log  0.94  is  9  —  o,  or  9. 

12.  The  arithmetical  complement  of  the  logarithm   (written  colog) 
of  a  number  is  the  logarithm  of  its  reciprocal,  and  is  found  by  subtract- 
ing each  figure  of  the  logarithm  from  9,  commencing  at  the  left,  except 
the    last   significant  figure  on  the  right,  which  is  subtracted  from   10. 

For  log  —  =  —  log  x—  10  —  log  x  —  10  ; 

OC 

thus,  if  log*=  2.46403,  colog^=  7.53597  —  10 ; 

if  \ogx  =  8.43000  —  10,  colog  x  =  1.57000. 

TABLE    XV. 

13.  Page  397  contains  the  logarithms  of  numbers  from  i  to  100,  to 
five  decimal  places. 

Pages  398-415  contain  the  mantissas  of  the  logarithms  of  numbers 
from  1000  to  10009,  to  five  decimal  places. 

Pages  416,417,  contain  the  mantissas  of  the  logarithms  of  numbers 
from  TOOOO  to  11009,  to  seven  decimal  places. 

NOTE. — The  mantissas  of  the  logarithms  of  numbers,  except  those  of  the  integral 
powers  of  10,  are  incommensurable,  the  mantissas  in  the  tables  being  found  as 
shown  in  Art.  I. 

To  find  the  Logarithm  of  a  Number. 

14.  The  characteristic  is  found  by  the  rules  in  Arts.  10  and  u,  and 
the  mantissa  from  the  tables,  as  shown  in  Arts.  15,  16,  17,  18. 

15.  When  the  number  has  four  figures.  —  Find  on  pages  398—415 
the  first  three  figures  in  the  column  marked  JVf  and  the  fourth  at  the  top 
of  one  of  the  other  columns.     The  last  three  figures  of  the  mantissa  are 
found  in  this   column  on   the   horizontal  line   through   the    first    three 
figures  of  the  given  number  in  column  N.     The  first  two  figures  of  the 
mantissa  are  those  under  L  in  the  same  line  with  the  number,  or  else 
those  nearest  above  it,  unless  the  last  three  figures  of  the  mantissa  as 
given  in  the  tables  are  preceded  by  a  *,  when  the  first  two  figures  are 
found  under  L  in  the  first  line  below  the  number.     Thus  (page  398), 

log  1136  =  3.05538;  log  1137  =  3.05576;  log  1138 -3.05614; 

log  1370  =  3.13672;  log  1371  =  3.13704;  log  1372  =  3.13735 ; 

log  1380  =  3.13988  ;  log  1381  =  3.14019  ;  log  1382  =  3.14051. 


EXPLANATION    OF    THE    TABLES.  389 

16.  When,  the  number  has  less  than  four  figures,  annex  ciphers  on 
the  right  and  proceed  as  in  Art.   15.     Thus, 

log  1.13  =  0.05308;  log  12.8=  1.10721  ;  log  130=  2.11394; 
log  15      =  1.17609;  log  16     =  1.20412  ;  log  17    =1.23045. 

17.  When  the  number  has  more  than  four  figures,  as    11.4672. — 
Since  the  mantissa  is  independent  of  the  position  of  the  decimal  point, 
point  off  the  first  four  figures   and   find  the  mantissa  of  log  1146.72. 
This  will  be  between  the  mantissas  of  log  1146  and  log  1147.     Hence 
find  from  the  tables  the  mantissas  corresponding  to    1146  and   1147; 
multiply  the  difference  between  them  (called  the  tabular  difference)  by 
.72,  and  add   the    product   (called    the    correction)   to    log  11.46;  the 
result  will  be  the  logarithm  required. 

Mantissa  of  log  1146  =  05918  log  11.46  =  1.05918 

Mantissa  of  log  1147  =  05956  correction  =  38  x  .72  =  27.36 

Tabular  difference      =        38  /.  log  11.4672  =  1.05945  36 

or  =  1.05945 

NOTE.  —  Since  any  mantissa  in  the  tables  may  be  in  error  by  half  a  unit  in  the 
fifth  decimal  place  (Art.  2),  no  advantage  is  gained  by  using  the  sixth  place  in 
the  interpolated  logarithm.  Thus,  according  to  Art.  I,  we  drop  the  .36,  and  call 
log  1 1. 4672  =  1.05945. 

NOTE.  — The  marginal  tables  should  be  used  in  multiplying  the  tabular  difference 
to  rind  the  correction  (Art.  4). 

NOTE.  — It  is  assumed  that  the  change  in  the  mantissa  is  proportional  to  that  in 
the  number,  as  the  latter  increases  from  1146  to  1147.  An  increase  of  I  in  the  num- 
ber causes  an  increase  of  38  in  the  mantissa;  hence  an  increase  of  .72  in  the  number 
will  cause  an  increase  of  38  X  .72  in  the  mantissa. 

NOTE.  — We  could  also  find  the  mantissa  of  log  11.4672  by  subtracting  the  prod- 
uct of  the  tabular  difference  by  .28  (or  i.oo  —  .72)  from  the  mantissa  corresponding 
to  1147;  that  is,  the  required  mantissa  is  05956  — (38 x  .28)  =05956— 10.64  — 05945 
as  before. 

18.  The  general  rule   is :    Find  the   mantissa   corresponding   to  the 
first  four  figures  of  the  number;  multiply  the  tabular  difference  by  the 
fifth  and  following  figures  treated  as  a  decimal ;  and  add  the  product 

to  the  mantissa  just  found. 

The  tabular  difference  is  the  difference  between  the  mantissas  corre- 
sponding to  the  two  numbers  in  the  tables,  between  which  the  given 
number  lies. 

log  1.62163  =  0.20995  ;  log 0.38024  =  1.58006  ;  ^0.0852763  =  2.93083; 
^189.524=2.27767;  Iogo.386o2  =  i.5866i  ;  ^0.0085938  =  3.93419; 
log  19983.4  =  4.30067  ;  ^3.98743  =  0.60070;  logo. 090046  =2.95446. 


390  EXPLANATION    OF    THE    TABLES. 

NOTE.  —  Page  397  is  used  when  the  number  contains  less  than  three  figures,  the 
number  being  found  in  the  column  N,  and  the  logarithm  in  the  column  headed  Log. 
The  characteristic  is  given  for  whole  numbers,  and  must  be  changed  for  decimals. 

NOTE. — When  a  number  is  composed  of  three  figures,  find  on  pages  398-415 
the  number  in  the  column  N,  and  the  mantissa  corresponding  in  the  column  L.  o. 

To  find  the  Number  corresponding  to  a  Given  Logarithm. 

19.  From  the  tables  we  find  the  sequence  of  figures  corresponding 
to  the  given  mantissa,  as  shown  in  Arts.  20,  21,  and  22,  the  position  of 
the  decimal  point  being  determined  by  the  characteristic  (Arts.  10,  n). 

20.  When  the  given  mantissa  can  be  found  in  the  tables.  —  Find  on 
pages  398-415  the  first  two  figures  of  the  mantissa  under  L  in  the  column 
headed  L.  o.     The  last  three  figures  of  the  mantissa  are  then  sought  for 
in  the  columns  headed  o,  i,  2,  •••  9,  in  the  same  line  with  the  first  two 
figures,  or  in  one  of  the  lines   just  below,  or  in  the  line  next  above 
(where  they  would  be  preceded  by  a  *).     The  first  three  figures  of  the 
required  number  will  be  found  in  the  column  headed  N,  in  the  same 
horizontal  line  with  the  last  three  figures  of  the  mantissa,  and  the  fourth 
figure  of  the  number  at  the  top  of  the  column  in  which  the  last  three 
figures  of  the  mantissa  are  found.     Thus  (page  398), 

0.06221  —  log  1.154  ;  0.06558  =  log  1.163  >  0.06893  =  l°g  1.172  ; 
0.07004  —  log  1.175  ;  0.07188  —  log  1.180;  0.08063  =  log  1.204. 

21.  When  the  given  mantissa  can  not  be  found  in  the  tables.  —  If  we 
wish  to  find  the  number  whose  logarithm  is  2.16531,  we  enter  the  tables 
with  16531,  and  find  that  it  lies  between  16524  and  16554,  so  that  the 
given  mantissa  corresponds  to  a  number  between  1463  and  1464.     Also 
16531  exceeds  16524  by  7,  and  this  difference,  divided  by  the  tabular 
difference  30,  gives  .23"-  as  the  amount  by  which  the  required  number 
exceeds  1463.     Hence  2.16531  =  log  I46.323---,  which  we  call  146.32, 
according  to  Art.  i,  the  incompleteness  of  the  tables  making  the  sixth 
figure  uncertain. 

NOTE. — The  marginal  tables  should  be  used  in  dividing  the  difference  between 
the  given  mantissa  and  the  one  next  less  in  the  tables  by  the  tabular  difference. 

22.  The  general  rule  is :    Find  the    number  corresponding   to    the 
mantissa  in  the  tables  next  less  than  the  given  mantissa  ;  divide  the 
excess  of  the  given   mantissa   over  the  one  found  in  the  tables  by  the 
tabular  difference;  and  annex    the   quotient  to    the  first  four  figures 
already  found. 

The  tabular  difference  is  the  difference  between  the  two  mantissas  in 
the  tables,  between  which  the  given  mantissa  lies. 

I.i66oo  =  log  0.14656  ;    0.18002  =  log  1.5136  ;    2.18200  =  log  152.06  ; 
1.19000  =  log  15.488  ;      4.19680  =  log  15773  ;     1.20020  =  log  15.856. 

23.  For  the  use  of  the  numbers  S',  T\  S",  T",  see  Arts.  35-38. 


EXPLANATION  OF  THE  TABLES.          391 


TABLE  XVI. 

24.  This  table  (pages  420-464)  contains  the  logarithms,  to  five  deci- 
mal places,  of  the  trigonometric  sines,  cosines,  tangents,  and  cotangents 
of  angles   from  o°   to  90°,  for  each  minute.     The    logarithms   in    the 
columns  headed  Z.  Sin,  L.  Tan,  and  L.  Cos,  are  augmented,  and  should 
be  diminished  by   10  (Art.   n),  while    those    in   the   columns   headed 
L.  Cot  are  correctly  given. 

25.  Since  sec^  = ,  and  cosec.#  =  - — ,  the  logarithms  of  the 

cos.* 


secant  and  cosecant  of  an  angle  are  the  arithmetical  complements  of 
those  of  the  cosine  and  sine  respectively  (Art.  12). 

To  find  the  Logarithmic  Functions  of  an  Angle  Less  than  90°. 

26.  When  the  angle  is  less  than  45°,  the  degrees  are  found  at  the  top 
of  the  page,  and  the  minutes  on  the  left.     The  numbers  in  the  same 
horizontal  line  with  the  minutes  of  the  angle  are  the  logarithmic  functions 
indicated  by  the  notation  at  the  top  of  the  columns.      Thus  (page  428), 

log  sin  8°  4'  =  9.14714  —  10,         log  tan  8°  4'  =  9.15145  —  10, 
log  cot  8°  4'  =  0.84855,  log  cos  8°  4'  =  9.99568  —  10. 

27.  When  the  angle  is  greater  than  45°,  the  degrees  are  found  at  the 
bottom  of  the  page,  and  the  minutes  on  the  right.     The  numbers  in  the 
same  horizontal  line  with  the  minutes  of  the  angle  are  the  logarithmic 
functions  indicated  by  the  notation  at  the  bottom  of  the  columns.     Thus 
(page  428), 

log  sin  81°  25'  —  9.99511  —  10,     log  tan  81°  25'  =  0.82120, 

log  cot  81°  25'=  9.17880  —  10,     log  cos  81°  25'  =  9.17391  —  10. 

28.  When   the  angle  is  given  to  decimals  of  a  minute.  —  In  finding 
log  sin  30°  8 '.48,    for    example,    we    see    that    it    will   lie    between    the 
logarithmic    sines    of   30°  8'  and  30°  9',  that  is,  between  9.70072  and 
9.70093,  their  difference  21   being  the  change  in  the  logarithmic  sine 
caused  by  a  change  of  if  in  the  angle.     Hence,  to  find  the  correction 
to  log  sin  30°  8'  that  would  give  log  sin  30°  8'.48  we  multiply  21  by  .48 
(Art.  4).     The  product  10.08  added  to  log  sin  30°  8',  since  log  sin  30°  9' 
is  greater  than  log  sin  30°  8',  gives  log  sin  30°  8 '.48  =  9.70082    (Art.  i). 
Similarly,    log  tan  30°  8'.48  =  9.76391,    log  cot  30°  8'.48  =  0.23609,  log 
cos  30°  8'.48  =  9.93691,   the    correction   being   subtracted    in   the   last 
two   cases,  since   the  cotangent  and  the  cosine  decrease  as  the  angle 
increases. 


392 


EXPLANATION    OF    THE    TABLES. 


29.  The  general  rule  is :  Find  the  function  corresponding  to  the  given 
degrees  and  minutes;  multiply  the  tabular  difference  by  the  decimals  of 
a  minute ;  add  the  product  to  the  function  corresponding  to  the  given 
degrees  and  minutes  when  finding  the  logarithmic  sine  or  tangent,  and 
subtract  it  when  finding  the  logarithmic  cosine  or  cotangent. 

The  tabular  differences  are  given  in  the  columns  headed  d.  and  c.  d., 
the  latter  containing  the  common  difference  for  the  L.  Tan  and  Z.  Cot 
columns.  The  difference  to  be  used  is  that  between  the  functions  cor- 
responding to  the  two  angles  between  which  the  given  angle  lies. 

For  30°  39'.38  :  log  sin  =  9.70747  ;  log  cos  =  9.93462  ; 

log  tan  =  9.77285  ;  log  cot  =  0.22715. 
For  59°  43 '.46:  log  sin  =  9.93632  ;  log  cos  =  9.70257  ; 

log  tan  =  0.233 75  ;  log  cot  =  9,76625. 

30.  When  the  angle  is  given  to  seconds,  the  correction  may  be  found 
by  multiplying  the  tabular    difference  by  the  number  of  seconds,  and 
dividing  the  product  by  60. 

To  find  the  Acute  Angle  corresponding  to  a  Given  Logarithmic 

Function. 

31.  The  column  headed  Z.  Sin  is  marked  L.  Cos  at  the  bottom,  while 
that  headed  L.  Cos  is  marked  L.  Sin  at  the  bottom  ;  hence,  if  a  logarith- 
mic sine  or  cosine  were  given,  we  should  expect  to  find  it  in  one  of  these 
two  columns.     Similarly,  we  should  expect  to  find  a  given  logarithmic 
tangent  or  cotangent  in  one  of  the  two  columns  headed  L.  Tan  and 
L.  Cot. 

32.  When  the  function  can  be  found  in  the  tables.  —  If  a  logarithmic 
sine  is  given,  find  it  in  one  of  the  two  columns  marked  L.  Sin  and 
L.  Cos ;  if  found  in  the  column  headed  Z.  Sin,  the  degrees  are  taken 
from  the  top,  and  the  minutes  from  the  left  of  the  page  ;   if  in  the 
column  headed  Z.  Cos  but  marked  Z.  Sin  at  the  bottom,  the  degrees 
are  taken  from  the  bottom,  and  the  minutes  from  the  right  of  the  page. 
Thus, 

9.70115  =  log  sin  30°  10';    9.93457  =  log  sin  59°  20'; 


9.93724  =  log  cos  30°  4';  9.70590  =  log  cos  59°  28'; 
9.76406  =  log  tan  30°  9';  0.23130  =  log  tan  59°  35' ; 
0.23420  =  log  cot  30°  15' ;  9.76870  =  log  <jpt  59°  35 '. 


33.  When  the  function  can  not  be  found  in  the  tables.  —  If  we  wish  to 
find  the  angle  whose  logarithmic  sine  is  9.70170,  we  see  on  page  450 
that  the  given  logarithmic  sine  lies  between  9.70159  and  9.70180,  and 


EXPLANATION    OF    THE    TABLES.  393 

hence  the  angle  is  between  30°  12'  and  30°  13'.  The  given  logarithmic 
sine  differs  from  log  sin  30°  12'  by  n,  and  this  difference,  divided  by 
the  tabular  difference  21,  gives  .52  +  as  the  decimal  of  a  minute  by 
which  the  angle  exceeds  30°  12'.  Hence  9.70170  =  log  sin  30°  12'. 52, 
which  we  call  30°  12'. 5,  since  the  incompleteness  of  the  tables  (Art.  i) 
makes  the  hundredths  of  a  minute  uncertain. 

34.  The  rule  is:  For  a  logarithmic  sine  or  tangent  find  the  degrees 
and  minutes  corresponding  to  the  function  in  the  tables  next  less  than 
the  given  function  ;  divide  the  difference  behi'cen  the  given  function  and 
t)ie  one  next  less  by  the  tabular  difference  ;  and  the  quotient  will  be  the 
decimal  of  a  minute  to  be  added  to  the  degrees   and   minutes   already 

found.  For  a  logarithmic  cosine  or  cotangent  find  the  degrees  and  min- 
utes corresponding  to  the  function  next  greater  than  the  given  function, 
since  tJie  cosine  and  cotangent  decrease  as  the  angle  increases,  and  divide 
the  difference  between  the  given  function  and  the  one  next  greater  by  the 
tabular  difference,  to  find  the  decimal  of  a  minute. 

The  tabular  difference  is  the  difference  between  the  two  functions  in 
the  tables,  between  which  the  given  function  lies. 

9.70000  =  log  sin  30°    4f.7;    9.93500  =  log  sin  59°  25'^  ; 

9.93400  =  log  cos  30°  47'.6  ;    9.70500  =  log  cos  59°  32'.2  ; 

9.77000  =  log  tan  30°  29'.  5  ;    0.23200  =  log  tan  59°  37 '.4  ; 
1  0.23300  =  log  cot  30°  19'.!  ;    9.76400  =  log  cot  59°  5 1 '.2. 

Angles  Near  o°  or  90°. 

35.  The  assumption  that  the  variations  in  the  functions  are  propor- 
tional to  the  variations  in  the  angles  if  the  latter  are  less  than  i '  fails 
when  the  angle  is  small,  shown  by  the  rapid  changes  in   the   tabular 
differences  on  pages  420,  421,  and  422. 

36.  The  quantities  S'  and  T'  which  are  used  in  this  case  are  defined 
by  the  equations 


where  «'  is  the  number  of  minutes  in  the  angle.  Their  values  from 
o°  to  i°  40'  (=100')  are  given  at  the  bottom  of  pages  397-415  ;  from 
i°  40'  to  3°  20'  at  the  left  margin  of  pages  398  and  399,  the  first  three 
figures  being  found  at  the  top ;  and  from  3°  to  5°  on  page  418.  Thus, 

for          i'=      i'   (page  399),  6"  =  6.46  373,  T' =  6.46  373; 

for        15'=     15'   (page  399),  ^'  =  6.46372,   T' =  6.46  373; 

for  2°4o'=i6o'   (page  399),  S'  =6.46  35 7,   T'  =  6.46  404  ; 

for  4°  20' =260'   (page  418),  S'  =  6.46  331,   7"  =  6.46  456. 
Each  of  these  numbers  should  have  —  10  written  after  it  (Art.  n). 


394  EXPLANATION    OF    THE    TABLES. 

NOTE.  —  The  logarithmic  cosine  of  a  small  angle  is  found  by  the  ordinary  method. 
The  cotangent  of  an  angle  is  the  reciprocal  of  the  tangent,  and  hence  the  logarithmic 
cotangent  is  the  arithmetical  complement  of  the  logarithmic  tangent.  The  formulas 
for  finding  the  logarithmic  cosine,  tangent,  and  cotangent  of  angles  near  90°  are 
given  on  page  419. 

37.  To  find  the  logarithmic  sine  or  tangent  of  a  small  angle.  —  From 
Art.  36,  we  have 

log  sin  «  =  S'  -j-  log  a', 

log  tan  a  =  T'  +  log  a'. 

Hence,  to  find  the  logarithmic  sine  or  tangent  of  an  angle  less  than 
5°,  find  the  value  of  the  S1  or  T'  corresponding  to  the  angle,  interpolat- 
ing if  necessary,  and  add  it  to  the  logarithm  of  the  number  of  minutes 
in  the  angle. 

Find  log  sin  o°42f.6.     Since  the  angle  is  nearer  43'  than  42',  we  take 

S'=  6.46  371 
log  42.6  =  1.62  941 

/.  log  sin  o°  42  '.6  =  8.09  3 1 2 

Find  log  tan  i°53'.2.  Since  the  angle  is  nearer  i°53'  (=  113')  than 
114',  we  take 

-  6.46  388 
log  113.2  =  2.05  385 

.-.  log  tan  i°  53 '.2  =  8.51  773 

NOTE.  —  When  the  angle  is  given  in  seconds,  either  reduce  the  seconds  to  deci- 
mals of  a  mymte,  or  use  the  values  of  S"  and  7'"  given  at  the  bottom  of  pages 
397-417  and  on  page  418.  They  are  defined  by  the  equations 

0 ./      ,       sin  a         i   ^i,       ,       tan  a 

S  "  —  log ,  and  T "  =  log , 

a"  a" 

where  a"  is  the  number  of  seconds  in  the  angle.     Hence 

log  sin  a  =  S"  +  log  a",  and  log  tan  a  =  T"  +  log  a". 

38.  To  find  the  small  angle  corresponding  to  a  given  logarithmic  sine 
or  tangent.  —  From  Art.  36, 

log  a'  =  log  sin  a  —  S', 
log  «'  =  log  tan  «  —  T'j 

or  log  a'  =  log  sin  a  -f  cpl  .S ', 

log  a'  —  log  tan  a  +  cpl  T'. 

When  the  angle  is  less  than  3°,  find  on  pages  420-422  the  value  of 
cpl,S'  (or  cpl  T')  corresponding  to  the  function,  interpolating  if  neces- 
sary, and  add  it  to  log  sin  a  (or  log  tan  a) ;  the  sum  will  be  the  loga- 
rithm of  the  number  of  minutes  in  the  angle. 

In  finding  the  angle  whose  logarithmic  sine  is  8.09006,  we  see  from 


EXPLANATION    OF    THE    TABLES. 


395 


the  L.  Sin  column  (page  420)  that  the  angle  is  between  o°  42'  and  o°  43', 
and  that  the  value  of  cpl  S'  must  be  either  3.53628  or  3.53629.  The 
given  logarithmic  sine  is  nearer  that  of  42'  than  that  of  43';  hence  we 

take 

cpl  S'  =  3.53628 
log  sin  a  =  8.09006 

log  «'=  1.62634    .*.  a' =  42'. 300. 

When  the  angle  is  between  3°  and  5°,  we  may  find  S'  and  T'  from 
page  418  after  finding  the  angle  approximately  from  pages  423  and  424. 
Thus  in  finding  the  angle  whose  logarithmic  tangent  is  8.77237  we 
find  from  page  423  that  the  angle  is  between  3°  23' and  3°  24',  being 
nearer  3°  23'.  Then  on  page  418  we  have 

T'  =  6.46423 
log  tan  a  =  8.77237 
.-.  log  tan  «—  T' =  log  «' =  2.30814     /.  «'=  203 '.30  =  3°  23'. 30. 


Angles   Greater  than  90  . 

39.  To  find  the  logarithmic  sine,  cosine,  tangent,  or  cotangent  of  an 
angle  greater  than  90°,  subtract  from  the  given  angle  the  largest  multi- 
ple of  90°  contained  therein.  If  this  multiple  is  even,  find  from  the 
tables  the  logarithmic  sine,  cosine,  tangent,  or  cotangent  of  the  remain- 
ing acute  angle.  If  the  multiple  is  odd,  the  logarithmic  cosine,  sine, 
cotangent,  or  tangent,  respectively,  of  the  remaining  acute  angle  will  be 
the  function  required  ;  thus,  sin  120°  =  sin  (90°  -f  30°)  —  cos  30°. 

1.     QUADRANT.          II.     QfADKANT.        III.     QUADRANT.          IV.     QUADRANT. 
x  =  a  180°  -f-  a  270°  -f-  a 


sin  x  = 
cos  .r  = 
tan  a  — 
cot  x  = 


-r  sin  a 
+  cos  a 
-f  tan  a 
-f  cot  a 


+  cos  a 

—  sin  a 

—  cot  a 

—  tan  a 


—  sin  a 

—  cos  a 
+  tan  a 

-f  cot  a 


—  cos  a 
+  sin  a 

—  cot  a 

—  tan  a 


Or  we  could  find  the  difference  between  the  angle  and  180°  or  360°, 
and  find  from  the  tables  the  same  function  of  the  remaining  acute 
angle  ;  thus,  cos  300°  =  cos  (360°  —  60°)  =  cos  60°,  etc. 


I.   QUADRANT. 

11.    QUADRANT. 

III.    QUADRANT. 

IV.    QUADRANT. 

X  = 

a 

i8o°-a 

180°  -  a 

36o°- 

or  - 

sin  x  = 

+  sin  a 

+  sin  a 

—  sin  a 

—  sin 

cos  .r  = 

+  cos  a 

—  cos  a                 —  cos  a 

+  cos 

tan  x  — 

+  tan  a 

—  tan  a 

-t-  tan  a 

—  tan 

cot  x  = 

+  cot  a 

—  cot  a                 +  cot  a 

—  cot 

To  indicate  that  the  trigonometric  function  is  negative,  n  is  written 
after  its  logarithm. 


396  EXPLANATION    OF    THE    TABLES. 

40.  To  find  the  angle  corresponding  to  a  given  function,  find  the 
acute  angle  a  corresponding  thereto,  and  the  required  angle  will  be  a, 
1 80°  ±  «,  or  360°  —  a,  according  to  the  quadrant  in  which  the  angle 
should  be  placed. 

41.  There  are  always  two  angles  less  than  360°  corresponding  to  any 
given   function.     Hence  there  will  be   ambiguity  in   the   result  unless 
some  condition  is  known  that  will  fix  the  angle ;   thus,  if  the  sine  is 
positive,  the  angle  may  be  in  either  of  the  first  two  quadrants,  but  if  we 
also  know  that  the  cosine  is  negative,  the  angle  must  be  in  the  second 
quadrant. 

Given  One  Function  of  an  Angle,  to  find  Another  without  finding 

the  Angle. 

42.  Suppose  log  tan  a  =  9.79361,  and  log  cos  a  is  sought.     On  page 
451   the  tabular  difference  for  log  tan  a  is  28,  and    that  for  log  cos  a 
is  8,  the  given  logarithmic  tangent  exceeding  9.79354  by  7.     Hence 
28:7  =  8:.*;    .•.  x=2=  correction    to    9.92905,    giving   log  cos  «  = 
9.92903. 

In  the  margin  are  tables  to  facilitate  the  process.  In  the  column 
headed  -fg,  the  numerator  is  the  tabular  difference  for  the  logarithmic 
cosines,  and  the  denominator  that  for  the  logarithmic  tangents1.  The 
correction  for  the  logarithmic  cosine  will  be  o  when  the  given  logarith- 
mic tangent  exceeds  the  next  smaller  logarithmic  tangent,  found  in  the 
tables,  by  less  than  1.8,  i  for  an  excess  between  1.8  and  5.2,  5  for  an 
excess  between  15.8  and  19.2,  etc.  In  the  example  above,  the  excess 
was  7,  which  is  between  5.2  and  8.8,  so  that  the  correction  is  2. 

For  example,  if  we  have  given  the  logarithms  of  the  sides  of  a 
right-angled  triangle,  log  a  =  2.98227  and  log  b  —  2.90255,  to  find  the 
hypotenuse,  we  use  the  formulas 

a        j  a  b 

tan  a  —  — ,  and  c  = 


b  sin  a      cos  a 

The  value  of  log  tan  a  being  found  in 

logtf  =  2.98227  (i)         the  column  marked  Z.  Tan  at  the  bot- 

.'.  log  sin  a  =9.88571  (4)         torn,  the  right  column  will  contain  the 

log  b  =  2.90255  (2)         logarithmic    sine    of    the   corresponding 

.-.  log  tan  «  =  0.07972  (3)         angle.     Also,  the  correction  to  9.88563 

.-.    log*:  =  3.09656  (5)         is  20  x  \\t  which  we  find  to  be  8  from 

the  table  headed  if. 

1  For  angles  <  45°. 


TABLE    XV. 

COMMON 

LOGARITHMS    OF    NUMBERS 

FROM     I     TO     IIOOO. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N.           Log. 

0 

2 

3 

— 

2O 

21 
22 
23 

1.30  103 

4O 

41 
42 
43 

i  .60  206 

6O 

61 
62 
63 

1-77815 

8O 

81 

82 
83 

1.90309 

o.ooooo 
0.30  163 

0.47712 

1.32  222 
1.34242 
I.36I73 

1.61  278 
1.62325 
I-63347 

1.78533 
1.79239 

1-79934 

1.90849 
1.91  381 
1.91  908 

4 
6 

0.60  206 

0.69  897 
0.77815 

24 

25 
26 

I.38O2I 

i-39  794 
1.41497 

44 
45 
46 

I-64345 
1.65321 
1.66276 

64 

65 
66 

1.80618 
1.81  291 
1.81  954 

84 

85 
86 

1.92428 
1.92942 
1-9345° 

I 

9 
IO 

ii 

12 
13 

0.84  510 

0.90  309 
0.95  424 

27 

28 

29 

30 

3i 
32 
33 

i-43  136 
1.44716 
1.46  240 

$ 

49 
5O 

52 
53 

1.6-  210 

1.68  124 
1.69020 

67 
68 
69 

7O 

72 
73 

1.82  607 
1.83251 
1.83885 

87 
88 
89 

90 

9i 
92 
93 

I-93952 
1.94448 

1-94939 

I.OOOOO 

1.47712 

1.69897 

1.84510 

1.95424 

1.04  139 

1.07  918 
i.  ii  394 

i-49  136 

i1^? 

1.70757 
1.71  600 
1.72428 

1.85  126 
1-85  733 
1.86332 

1.95904 
1.96379 
1.96848 

H 
15 

16 

.14613 
.17609 
.20412 

34 
35 
36 

1.53  148 
1.54407 
I-55630 

54 

P 

I-73239 
1.74036 
1.74819 

74 
75 
76 

1.86  923. 
1.87  506 
i.  88  08  1 

94 
95 
96 

I.973I3 
1.97772 
1.98227 

18 

19 

20 

-23  045 
•25  527 
•27  875 

37 
39 
4O 

1.56820 
I-57978 
1.59106 

3 

59 
6O 

I-75587 
I-76343 
1.77085 

77 
78 
79 

8O 

i  .88  649 
1.89209 
1.89763 

97 
98 

99 
100 

1.98677 
1.99-123 
1.99564 

1.30  103 

i.  60  206 

I.778I5 

1.90309 

2.OOOOO 

S'.              T'. 

S".              T". 

o'           6.46  373             373 

o°    o'=     o"             4-68557             557 

1                     373             373 

o      i   =    60                       557             557 

o      2  =  120                       557             557 

(397) 


398 


S'.  T'. 

6  '& 

N, 

L,    0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

366 

385 

100 

ooooo 

043 

087 

130 

173 

217 

260 

303 

346 

389 

44      43      4Q 

366 

38s 

IOI 

432 

475 

518 

561 

604 

647 

689 

732 

775 

817 

366 
366 

385 
386 

1  02 
103 

860 

oi  284 

903 
326 

945 
368 

988 
410 

452 

494 

*ii5 
536 

*'57 
578 

*i99 
620 

662 

2 

3 

4-4   4-3    4-2 
8.8    8.6    8.4 
13.2  12.9  12.6 

366 

386 

104 

703 

745 

787 

828 

870 

912 

953 

99.9 

"=036 

*O78 

17.6  17.2  16.8 

;366 

386 

105 

02  119 

1  60 

202 

243 

284 

325 

366 

407 

449 

490 

c 

22.O  21.  C  2I.O 

366 

386 

106 

531 

572 

612 

653 

694 

735 

776 

816 

857 

898 

6  26.4  25.8  25.2 

366 

387 

107 

938 

979 

*oi9 

*o6o 

*IOO 

*i4i 

*i8i 

*222 

*262 

*302 

730.830.1  29.4 

1365 

387 

108 

03342 

383 

423 

463 

.503 

543 

583 

623 

663 

703 

8  35-2  344  33-6 

365 

3«7 

109 

743 

782 

822 

862 

902 

941 

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6-46  373      373 

o°    2'=   120"  4-68557     557 

o°2S'=i6So"    4.68557 

2 

373      373 

o      3  =   1  80             557      557 

o    29  =  1  740 

557     559 

15 

372      373 

o      4  =   240             557      558 

o    30  =  1  800 

557    559 

20 

372      373 

o    25  =1500             557      558 

o    31  =1860 

557    559 

o    26=1560             557      558 

o    32  =  1920 

557    559 

o    27=1620             557      55s 

o    33=1980 

557    559 

o    28=1680             557      558 

o    34  =2040 

557 

400 


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P,  P, 

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3     373  373 

o°  3'=  i 
04=2 

S."  T." 
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40     557  558 
30      557  558 

o°  2 
o  2 
o  3 

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7  =  22 

S."  T." 
60"  4.68  557  559 
20     557  559 
80     557  559 

20     372  373 
25     372  373 

05-3 

8  =  22 

o  33  =  1980      557  559 
o  34  =  2040     557  559 
o  35  =  2100      557  559 
o  36  =  2160     557  559 

o  39-2340     557  559 
o  40  =  2400     557  559 
o  41  =  2460     556  560 
o  42  =  2520     556  560 

401 


N, 

L,  0  i   1    2    3    4 

5    6 

7    8 

9 

P.P. 

250 

25  1 
252 

253 
254 
255 
256 

257 
258 

259 
26O 

261 
262 
263 

264 
265 
266 
267 
268 
269 

27O 

271 
272 
273 
274 
275 
276 

277 
278 
279 

28O 

281 
282 
283 
284 

288i 

287 
288 
289 

290 

291 

292 
293 
294 
295 
296 

297 
298 
299 
300 

39794 

811 

829   846 

863 

881 

898 

9*5 

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4 

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2 

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4 

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9 

2 

3 
4 

8 
9 

18 
1.8 
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54 
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10.8 

12.6 

14.4 
16.2 

17 

i-7 
34 

6^8 

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16 

1.6 

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12.8 

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15 

3-° 

4-5 
6.0 

7-5 
10.5 

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1.4 

2.8 

4.2 

5-6 
7.0 
8.4 
9-8 

II.  2 

12.6 

967 
40140 
312 

483 
654 

824 

993 
41  162 

33° 

985 
157 
329 
500 
671 
841 

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179 
347 

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175 

346 
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688 
858 

196 
363 

192 

364 

535 
705 

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212 
380 

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209 

552 
722 
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229 
397 

226 
398 

569 
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246 
414 

243 

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756  ! 
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263 

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261 
432 
603 
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280 
447 

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278 
449 
620 
790 
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296 
464 

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637 
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481 

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547 

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581 

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647 

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830 
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42  160 

325 

488 

975 
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667 
830 

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697 

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193 

357 
521 
684 
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880 

210 

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537 
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731 

896 

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226 
390 

553 
716 

878 

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243 
406 

570 

732 
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423 
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780 
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275 
439 
602 

765 
927 
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797 
963 

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292 

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619 

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814 
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308 
472 
635 
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959 

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152 

165 

185 

20  1 

217 

233 

249 

265 

281 

297 

457 
616 

775 
933 
44091 

248 
404 
560 

473 
632 

791 

949 
107 

264 
420 
576 

329 
489 
648 

807 
965 

122 

279 
436 

592 

345 
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823 
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138 

295 

45  i 
607 

361 
521 
680 

838 
996 
154 

311 

467 
623 

377 
537 
696 

854 

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326 
483 
638 

393 
553 
712 

870 

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185 

342 
498 
654 

409 
569 
727 
886 

20  1 
358 

425 
584 
743 
902 

217 

373 

529 
685 

441 
600 
759 
917 

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232 

389 
545 
700 

716 

73i  I  747 

762 

778 

793 

809 

824 

840 

855 

871 

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17.9 

332 
484 

637 
788 

939 
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886 
040 
194 

347 
500 
652 
803 
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105 

902 
056 
209 

362 

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667 

818 
969 

120 

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225 

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530 
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135 

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255 
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423 
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180 

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286 

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195 

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148 
301 

454 
606 

758 
909 
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210 

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163 

469 
621 

773 

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225 

240 

255 

270 

285 

300 

315 

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345 

359 

374 

389 
538 

835 
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47  129 
276 
422 
567 

404 

553 
702 

850 

997 
144 

290 
436 

582 

419 
568 
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864 
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159 
305 
451 
596 

434 
583 

879 

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465 

611 

449 
598 
746 

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1  88 

334 
480 

625 

464 

613 

761 

909 
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202 

349 
494 
640 

479 
627 

776 

923 
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217 

363 
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654 

494 
642 
790 

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232 

378 
524 
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509 

657 
805 

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246 

392 

538 
683 

523 
672 
820 

967 
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261 
407 

553 
698 

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L.  0    1     23 

4 

567 

8 

9 

P.  P, 

S.'  T.' 
2'  6.46  373  373 
3     373  373 

S."  T." 
o°  4'=  240"  4-68557  558 

o  5  =  300      557  558 

0°  < 

o 

S."  T." 
15'  =2700"  4.68556  560 
0  =  2760      556  560 
4.7  =  2820      556  560 
l8  =  2880     556  560 
19  =  2940      556  560 
50  =  3000      556  561 

25      372  373 
26     372  373 

27     372  374 
30     372  374 

041=  2460      556  560 
o  42  —  2520      556  560 
o  43  =  2580      556  560 
o  44  =  2640      556  560 
o  45  =  2700      556  560 

o 

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o  < 

0 

R'M'D  SURV.  —  26 


402 


N, 

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1 

2 

3    4 

5 

6 

7    8  |  9 

pTp!   | 

300 

301 
302 
303 
3°4 
305 
306 

307 
308 

3°9 
310 

311 
312 

3U 

3H 

315 
316 

317 
3i8 

319 
320 

321 

322 
323 
324 
325 
326 

327 
328 

329 
330 

33i 
332 
333 
334 
335 
336 

337 
338 
339 
34O 

34i 

342 
343 
344 
345 
346 

347 
348 
349 
350 

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727 

74i 

756 

770 

784 

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15 

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2.8 

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7.0 
8.4 
9.8 

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12.6 

13 

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2.6 

3-9 

5.2 

6-5 
7-8 
9-i 
10.4 
11.7 

12 

1.2 

2.4 

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4.8 
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10.8 

857 
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144 
287 
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855 
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871 
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159 
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728 
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885 
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173 
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458 
601 

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900 
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187 

330 
473 
615 

756 
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914 
058 
202 

344 
487 
629 
770 
911 

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929 
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216 

359 
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643 

785 
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943 
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230 

373 
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244 

387 
530 
671 

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954 
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972 
116 
259 
401 

544 
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986 
130 
273 
416 
558 
700 

841 

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164 

178 

192 

206 

220 

234 

248 

262 

276 
415 
554 

693 
831 
969 

50  106 
243 
379 

290 
429 

568 

707 

845 
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120 
256 

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443 
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147 
284 
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332 

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610 

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161 

297 
433 

346 
485 
624 

762 
900 
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174 
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447 

360 

499 
638 

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914 
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1  88 

325 
461 

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651 

790 
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202 
338 
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803 
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215 

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955 

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229 

365 
501 

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529 

542 

556 

569 

583 

596 

610 

623 

637 

651 
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920 

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322 

455 
587 
720 

664 
799 
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068 
202 
335 
468 
601 
733 

678 
813 
947 
081 
215 
348 
481 
614 
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691 
826 
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095 
228 
362 

495 
627 

759 

705 
840 

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108 
242 
375 
508 
640 
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718 
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987 

121 

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654 
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732 
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135 
268 
402 

534 
667 

799 

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880 
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148 
282 
415 
548 
680 
812 

759 
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162 

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428 

561 
693 
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772 
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175 
308 

441 

574 
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838 

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865 

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127 

257 
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140 
270 
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530 
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284 

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543 
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1  66 

297 

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179 
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192 
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711 
840 

969 

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205 

336 

466 
595 
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218 
349 

479 
608 

737 
866 
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122 

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231 

362 

492 
621 

750 
879 
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148 

161 

173 

1  86 

199 

212 

224 

237 

250 

263 

275 
403 
529 
656 
782 
908 

54033 
158 

283 

288 

415 
542 
668 

794 
920 

045 
170 

295 

301 
428 
555 
68  1 
807 
933 
058 
183 
307 

3H 
441 

567 

694 
820 

945 
070 

195 
320 

326 

453 
580 

706 
832 
958 
083 
208 
332 

339 
466 

593 
719 
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095 
220 

345 

352 
479 
605 

732 

857 
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1  08 
233 

357 

364 
491 
618 

744 
870 

995 
1  20 
245 
37° 

377 
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631 

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133 

382 

390 

r7 
643 

769 
895 

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H5 
270 

394 

407 

419 

432 

444 

456 

469 

481 

494 

506 

518 

N, 

L,  0    1 

2 

3 

4 

5 

6 

7 

8 

9 

P,  P, 

S.'   TV 
3'  646  373  373 

4     373  373 

S."  T." 
o°  5'=  300"  4-68557  558 

o  6  =  360      557  558 

o°  54'  =3 
o  55  =  3 

S."  T." 
240"  4.68  556  561 
300     556  561 
360     556  561 
420     555  561 
480     555  562 
540     555  562 

30     372  374 
35     372  374 

o  50  =  3000      556  561 
051=  3060      556  561 
o  52  =  3120      556  561 
o  53  =  3I8o      556  561 
o  54  =  3240      556  561 

o  56-3 
0  57  =  3 
o  58  =  3 
o  59  =  3 

403 


t  N.   L,  0    1    23 

4 

5  J  6    7    8  |  9 

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351 

352 
353 

354 
355 
356 

357 
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359 
360 

361 
362 

363 
364 
365 
366 

367 

368 

369 
37O 

37i 
372 
373 
374 

9 

377 
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379 
380 

38i 
382 
383 
384 
385 
386 

387 
388 
389 
39O 

39i 

392 
393 
394 
395 
396 

397 
398 
399 
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54407   419   432   444 

456 

469 

481 

494 

506 

518 

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12 

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4.8 
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7-2 
8.4 
9.6 
10.8 

11 
i.i 

2.2 

3-3 
4-4 

8 

11 

9-9 
10 

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2.0 

3-o 

4.0 

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6.0 
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654 
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315 
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593 
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206 

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449 
570 

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728 
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230 

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133 
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376 
497 
618 

630   642 

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666 

678 

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703 

715 

727 

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229 
348 
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360 
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253 
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146 
265 
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158 

277 
396 

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632 

750 

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170 
289 
407 

526 

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761 

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301 
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538 
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194 
312 
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549 
667 

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847 
967 

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205 
324 
443 

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217 
336 
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573 
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808 

820 

832 

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902 

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937 
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171 

287 
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634 
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183 
299 
415 
530 
646 
761 
875 

961 
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194 

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426 

542 

657 
772 
887 

972 
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206 

322 
438 

553 
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217 

334 
449 
565 
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795 
910 

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229 

345 
461 

576 
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807 
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124 
241 

357 
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136 
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148 
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104 
218 
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557 
670 

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229 

343 
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569 
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127 
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161 
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172 
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625 

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184 
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195 
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59  106   1  1  8 

129 

140 

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162   173 

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207 

218 
329 
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550 
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770 

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262 
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152 

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295 
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306 
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249 

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S.'  T.' 
3'  6.46  373  373 
4     373  373 

o°  5'-  2 
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S."  T." 
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»6o      557  558 
20      557  55s 

o 

i'=3< 

2  =  3 

S."  T." 
36o"  4-68555  562 
720      555  562 
jSo      555  562 
HO      555  563 
P°      555  563 
?6o      555  563 
320      555  563 

35      372  374 
39     372  374 
40     372  375 

o  7  -  A 

o  58  =  3480      555  562 
o  59  =  3540      555  562 
i  o  =  3600      555  562 
i  i  =  3660     555  562 

4-3: 

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6  =  3< 
7  =4< 

N,  |  L.  0  |   1    2 

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4 

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6 

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P.P. 

400 

401 
402 
403 
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405 
406 

407 
408 
409 

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411 
412 
413 
414 

415 
416 

417 
418 
419 

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421 
422 
423 
424 

425 
426 

427 
428 
429 

430 

43i 
432 
433 
434 
435 
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437 
438 
439 
440 

441 
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60  206 

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342 

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40     372  375 
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43     371  375 
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45     37i  375 

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11—42 

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i  7  =  4020     555  563 
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40      557  558 

0  i8'  =  46 
19  =47 

S."  T." 
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60      553  566 
20      553  566 
80      553  566 
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45      37i   375 
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49     371   376 
50     371   376 

o   9=1 

' 

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Ji  =48 
>2  =49 

23  =49 

24  =50 

i  15  =4500     554  564 

i  16  =456°      554  565 
i  17  =4620     554  565 
i  18  =4680     554  565 

406 


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S."  T." 
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o 

26'=  5 

27  =  5 

S."  T." 
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220     553  567 
280     553  567 
340     553  567 
400     553  567 
460     552  568 
520     552  568 

5°     37i  376 
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O  IO  =  6 

28-5 

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i  24  =  5040      553  566 
i  25  =  5100     553  566 
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29-5 
30  =  5 

3i  =5 

32-5 

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772 

195 

269 

342 

4i5 

488 
561 

634 
706 

779 

203 
276 
349 
422 

495 
568 

641 
7H 
786 

2IO 
283 

357 
430 
5°3 
576 
648 
721 
793 

217 
291 
364 
437 
510 
583 
656 
728 
801 

22? 
298 
371 

444 
517 
590 

663 

735 
808 

815   822   830   837 

844 

851   859 

866 

873 

880 

N. 

L,  0  |   1    23 

4 

5 

6    7 

8 

9 

P 

.  P. 

S.'  T.' 
6'  6.46  373  373 

S."  T." 
o°  9'=  540"  4.68  557  558 
o  10  =  600     557  558 

i°3 
1  3 

5'=  57 

S."  T." 
oo"  4.68  552  569 
60      552  569 

20        552  569 
80        552  569 

40      55  r  569 
oo      551  570 

55     371  376 
56     37i  376 
57     37i  377 
58     371  377 
59     370  377 
60     370  377 

o-57 
7  =  58 
8  =  58 

9  =  59 
o  =  60 

i  31  =  5460     552  568 
i  32  =  5520      552  568 
i  33  =  558o      552  568 
i  34  =  5640      552  568 
i  35  =  5700      552  569 

i  3 
i  3 
1  3 

i  4 

408 


1  N> 

L,  0 

1 

2    3 

4 

5  |  6 

7 

8 

9 

P.P. 

GOO 

601 
602 
603 
604 
605 
606 
607 
608 
609 

610 

611 
612 
613 
614 
615 
616 
617 
618 
619 

620 

621 
622 
623 
624 
625 
626 
627 
628 
629 

630 

631 
632 
633 
634 
635 
636 

637 
638 

639 
640 

641 
642 
643 
644 

645 
646 

647 
648 
649 

65O 

77815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

2 

3 
4 

8 
9 

i 

2 

3 
4 

6 

I 

9 
i 

2 

3 

4 
5 
6 

8 
9 

8 

0.8 
1.6 
2.4 
3-2 
4.0 
4.8 

5-6 
6.4 
7.2 

7 
0.7 
1.4 

2.1 

2.8 

3-5 
4.2 

4-9 
5.6 

6-3 

6 

0.6 

1.2 

1.8 
2.4 

3-0 
3-6 
4.2 
4.8 
5-4 

887 
960 
78032 
104 
176 
247 

3J9 

390 
462 

895 
967 

039 
in 
183 

254 
326 
398 
469 

902 

974 
046 

118 
190 
262 

333 
405 
476 

909 
981 
053 

125 
197 
269 

340 
412 
483 

916 
988 
06  1 
132 
204 
276 

347 
419 
490 

924 
996 
068 
140 

211 

283 

355 
426 

497 

93  i 
*oo3 

075 
147 
219 
290 

362 
433 
504 

938 

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082 

'54 

226 

297 

369 
440 

512 

945 
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089 
161 
233 
305 
376 
447 
S19 

952 

*025 

097 

1  68 
240 
312 

383 
455 
526 

533 

540 

547 

554 

561 

5<>9 

576 

583 

590 

597 

604 

675 
746 

817 
888 
958 
79029 
099 
169 

611 
682 
753 
824 
895 
965 
036 
106 
176 

618 
689 
760 

831 
902 
972 

043 
"3 

183 

625 
696 
767 

838 
909 
979 
050 

120 
I90 

633 
704 

774 

845 
916 
986 

057 
127 
197 

640 
711 
781 
852 
923 
993 
064 

134 
204 

647 
718 
789 

859 
930 
*ooo 

071 
141 

211 

654 

725 
796 

866 

937 
*oo7 

078 
148 
218 

661 

732 
803 

873 
944 
*oi4 

085 

155 
225 

668 

739 
810 

880 

95  i 

*O2I 
092 
162 
232 

239 

246 

253 

260 

267 

274 

28l 

288 

295 

302 

309 
379 
449 
518 

588 
657 
727 
796 
865 

3i6 
386 

456 
525 
5?5 
604 

734 
803 

872 

323 
393 
463 

'532 
602 
671 
741 
810 
879 

330 
400 

47° 

539 
609 
678 

748 

817 
886 

337 
407 

477 
546 
616 

685 

754 
824 

893 

344 
414 

484 

553 
623 
692 
761 

831 
900 

351 

42I 

49  i 
560 
630 
699 
768 

837 
906 

358 
428 
498 

f7 
637 
706 

775 
844 
9i3 

365 
435 
505 

574 
644 

7i3 
782 
851 
920 

372 
442 

5" 

58i 
650 

720 
789 
858 
927 

934 

941 

948 

955 

962 

969 

975 

982 

989 

996 

80003 
072 
140 
209 
277 
346 
414 
482 
55° 

010 

079 
H7 

216 

284 
353 
421 
489 

557 

017 

085 
154 
223 
291 
359 
428 
496 
564 

024 
092 
161 
229 
298 
366 

434 
502 

570 

030 
099 
1  68 
236 
3°5 
373 
441 
509 
577 

037 

106 

175 

243 
312 

380 
448 
516 

584 

044 

"3 

182 

250 
3i8 
387 
451 
523 
59i 

951 

1  20 

1  88 

257 
325 
393 
462 
530 
598 

058 
127 

J95 
264 
332 
400 

468 
536 
604 

065 

134 
202 

271 

339 
407 

475 
543 
611 

618 

625 

632 

638 

645 

652 

659 

665 

672 

679 

686 

754 
821 

889 

956 
81  023 

090 

158 
224 

693 
760 
828 

895 
963 
030 

097 
164 
231 

699 
767 
835 
902 
969 
037 
104 
171 
238 

706 

774 
841 

909 
976 
043 
ii  i 

178 
243 

7^3 

781 
848 
916 

983 
050 

117 

184 
251 

720 
787 
855 
922 
990 
057 
124 
191 
258 

726 

794 
862 

929 
996 
064 

131 

198 
265 

733 
80  r 
868 

936 

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070 

137 

204 
271 

740 
808 
875 
943 

*OIO 

077 

144 

211 

278 

747 
814 
882 

949 
*oi7 
084 

1S1 

218 

28! 

291 

298 

305 

3" 

3i8 

325 

33i 

338 

345   35i 

N, 

L,  0 

1 

2 

3 

4 

5    6 

7 

8    9 

P,  P, 

S.'   T.' 
6  6.46  373  373 

7     373  373 

S."  T." 
o°  io'=  600"  4.68  557  558 
011=  660     557  558 

0  44'  =  62 

45  =63 

S."  T." 
40"  4.68  551  571 
00      551  571 
60      55i  57i 
20      550  572 
80      550  572 
40      55°  572 

60     370  377 
63     37°  377 
64     37°  378 
65     37°  378 

40  =6000     551   570 
41  =6060     551   570 
42  =6120     551   570 
43  =6180      551   570 
44  =6240      531   571 

46  =63 

47  =64 
48  =64 
49  =65 

409 


N. 

L,  0 

I 

23    4 

5    6 

7    8 

Q 

P 

,  P, 

650 

651 
652 
653 
654 

§i 

III 

659 
66O 

661 

662 
663 
664 

s 

667 

668 
669 

67O 

671 

672 
673 
674 

675 
676 

677 
678 
679 

680 

681 
682 

G35 
680 
687 
688 
689 

690 

691 
692 
693 
694 

|695 
696 

697 
698 

699 

7OO 

81  291 

298 

305   311   348 

325   33i   338   345 

351 

i 

2 

3 
4 

1 

8 
9 

i 

2 

3 

4 

8 
9 

7 
0.7 
1.4 

2.1 
2.8 

3-5 
4.2 

4-9 
5-6 
6-3 

6 

0.6 

1.2 

1.8 

2-4 

3-o 
3-6 
4.2 
4.8 
54 

358 
425 

49  i 

558 
624 
690 

757 
823 
889 

365 
43i 
498 

564 

63  I 
697 

763 
829 

895 

37i 

438 
505 
57i 
637 
704 

77° 
836 
902 

378 
445 
5" 

17S 
644 

710 
776 
842 
908 

385 
45i 
518 

584 
651 
717 

783 
849 
9i5 

39i 
458 
525 
59i 
657 
723 
790 
856 
921 

398 
465 
53i 
598 
664 
730 
796 
862 
928 

405 
47i 
538 
604 
671 

737 
803 
869 

935 

411 
478 
544 
611 
677 
743 
809 

875 
941 

418 
485 
55i 
617 
684 
750 
816 
882 
948 

954   961 

968 

974 

981 

987 

994 

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82020 
086 
151 
217 
282 
347 

413 
478 
543 

027 
092 
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223 
289 

354 
419 

484 
549 

033 
099 
164 
230 

2g 
360 

426 
491 
556 

040 
105 
171 

236 
302 

367 

432 
497 
562 

046 

112 
I78 

243 
308 

373 
439 
5°4 
569 

053 
119 
184 

249 
315 
380 

445 
510 

575 

060 

125 
191 

256 
321 

387 
452 

5'7 

582 

066 
132 
197 

263 
328 

393 

458 

523 
588 

073 
138 
204 

269 

334 
400 

465 
530 

595 

079 

145 

210 

276 

34i 

406 

47i 
536 
601 

607 

614 

620 

627 

633 

640 

646 

653 

659 

666 

672 

737 
802 

866 
930 
995 
83059 
123 

187 
251 
31! 
378 
442 

506 
569 
632 

696 

759 
822 

679 

743 
808 

872 
937 

*OOI 

065 
129 
»93 

685 

750 
814 

879 

943 
*oo8 

072 

136 
200 

692 

756 
821 

885 

95° 
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078 
142 
206 

698 
763 
827 
892 
956 

*O2O 
085 
149 
213 

705 
769 
834 
898 
963 

*O27 

091 

155 
219 

711 
776 
840 
905 
969 
"033 

097 
161 
225 

718 

$ 

911 

975 
*040 

104 
1  68 
232 

724 
789 
853 
918 
982 
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no 
174 
238 

730 
795 
860 

924 

988 

*052 
117 

181 

245 

257 

264 

270 

276 

283 

289 

296 

302   308 

321 

383 
448 

5'2 

575 
639 
702 

765 
828 

327 
39i 
455 
518 
582 
645 
708 
77i 
835 

334 
398 
461 

525 
588 
651 

778 

841 

340 

404 
467 

531 

594 
658 

721 

784 
847 

347 
410 

474 

537 
601 
664 

727 
790 

853 

353 
4i7 
480 

544 
607 
670 

734 
797 
860 

359 
423 
487 

550 
613 
677 
740 
803 
866 

366 
429 
493 

556 
620 
683 

£9 
872 

372 
436 
499 

563 
626 
689 

1% 

879 

885   891   897 

904 

910 

916 

923 

929 

935 

942 

948 
84011 

073 
136 
198 
261 

323 
386 
448 

954 
017 
080 

142 
205 
267 

330 
392 
454 

960 
023 
cS6 

148 

211 

273 
336 
398 

460 

967 
029 
092 

155 
217 
280 

342 
404 
466 

973 
036 
098 
161 
223 
286 

348 
410 

473 

979 

042 
105 
167 
230 
292 

354 
417 
479 

985 
048 
in 

173 
236 
298 

36i 
423 

4*3 

992 

055 
117 

1  80 
242 
305 
367 
429 
491 

998 
06  1 
123 
1  86 
248 
3" 
373 
435 
497 

*004 
067 
130 
192 

251 

317 

379 
442 

5°4 

5!o   516 

522  i  528   535 

54i   547   553   559   566 

1  N. 

L.  0    1     2    3    4 

5 

6789      P 

.  P, 

S.'  T.' 
6'  6.46373  373 

7      373  373 

0° 
0 

S."  T." 
io'=  600"  4.68  557  558 
ii  =  660      557  558 
12  =  720      557  55S 

°5 

5 
5 

l':=66 

2-67 

T." 
60"  4-68550  573 
20      550  573 
80      550  573 
40      55°  573 
oo      549  574 
60      549  574 
20      549  574 

65     37°  378 
69     370  378 
7°     37°  379 

o 

3-67 

I  48  =  6480     550  572 
i  49  =  6540      550  572 
i  50  =  6600      550  572 
i  51  =6660      550  573 

54  =  6* 
55  =  65 
56  =  65 

i  57  =  7C 

410 


N. 

L,  0    1 

23456 

7 

8  |  9 

P.  P. 

7OO 

701 

702 
703 
704 

3 
$ 

709 

7IO 

711 
712 
7U 
714 

7i5 
716 

717 

718 
719 

720 

721 

722 
723 
724 

725 
726 

727 

728 

729 
730 

73i 

732 
733 

734 
735 
736 

737 
738 
739 
74O 

74i 
742 
743 
744 
745 
746 

747 
748 
749 
750 

84  510 

516 

522 

528 

535 

54i 

547 

553 
615 
677 
739 
800 
862 
924 

985 
046 
107 

559 

566 

i 

2 

3 
4 

5 
6 

8 
9 

i 

2 

3 
4 

i 

8 
9 

i 

2 

3 
4 

6 

8 

9 

7 
0.7 
1.4 

2.1 

2.8 

3-5 
4-2 

4.9 

5-6 
0-3 

6 

0.6 

1.2 

1.8 

2.4 

3i6 

4-2 

4.8 

5-4 

5 

o-5 

I.O 

i-5 

2.O 

2-5 

3-o 
3-5 
4.0 

4-5 

572 
634 
696 

757 
819 
880 

942 
85  003 
065 

578 
640 
702 

763 

825 

887 

948 
009 
071 

584 
646 
708 
770 
831 
893 

954 
016 
077 

590 
652 
714 
776 

837 
899 

960 

022 
083 

597 
658 
720 
782 
844 
905 
967 
028 
089 

603 

Is 

788 
850 
911 

973 
034 
095 

609 
671 
733 

794 
856 
917 

979 
040 

IOI 

621 

683 
741 
807 
868 
930 
991 
052 
114 

628 
689 
75i 
813 
874 
936 

997 
058 
1  20 

126 

132 

138 

144 

'5° 

156 

163 

169 

i?5 

181 

187 
248 
309 
37° 
43i 
491 

552 
612 

673 

193 
254 
315 
376 
437 
497 

558 
618 
679 

199 
260 
321 

382 
443 
503 

564 
625 

685 

205 
266 
327 
388 

449 
509 

570 
631 
691 

211 

272 

333 
394 
455 
5'6 
576 
637 
697 

217 
278 
339 
400 
461 
522 
582 
643 
7°3 

224 
285 
345 
406 
467 
528 
588 
649 
709 

230 
291 
352 
412 
473 
534 
594 
655 
715 

236 
297 
358 
418 
479 
540 
600 
66  1 
721 

242 
303 
364 
425 
485 
546 
606 
667 
727 

733 

739 

745 

75i 

757 

763 

769 

775 

781 

788 

794 
854 
914 

974 
86034 
094 

153 
213 

273 

800 
860 
920 
980 
040 

IOO 

159 
219 
279 

806 
866 
926 
986 
046 
1  06 
165 
225 
285 

812 
872 
932 

992 
052 

112 
171 
231 
291 

818 
878 
938 

998 
058 
118 
177 
237 
297 

824 
884 
944 
*OO4 
064 
124 

183 
243 
303 

830 
890 
9?o 

*OIO 

070 

130 
189 

249 

308 

836 
896 
956 
*oi6 
076 
136 

195 

255 
3H 

842 
902 
962 

*O22 
082 
141 
201 
26l 
320 

848 
908 
968 

*028 

088 

J47 
207 
267 
326 

332 

338 

344 

35° 

356 

362 

368 

374 

380 

386 

392 
45i 
5io 

57° 
629 
688 

747 
806 
864 

398 

457 
516 

576 
631 
694 

753 
812 
870 

404 

463 

522 

581 
641 
700 

759 
817 

876 

410 

469 
528 

587 
646 

7°5 
764 
823 
882 

41^ 

475 
534 

593 
652 
711 
770 
829 
888 

421 

481 
540 

599 
658 
717 
776 

835 
894 

427 

487 

546 

605 

664 

723 
782 

841 
900 

433 
493 
552 
611 

670 
729 
788 

847 
906 

439 
499 
558 
617 
676 
735 
794 
853 
911 

445 
5°4 
564 
623 
682 
741 
800 

859 
917 

923 

929 

93? 

941 

947 

953 

958 

964 

970 

976 

982 
87  040 
099 

'57 
216 
274 

332 
390 
448 

988 
046 
105 

163 

221 

280 

338 
396 

454 

994 
052 
in 

169 
227 
286 

344 
402 
460 

999 
058 
116 

175 

233 
291 

349 
408 
466 

*oo5 
064 

122 

181 
239 
297 
355 
4U 
47i 

*OII 

070 

128 
186 
245 
303 

36i 
419 

477 

*oi7 
075 
134 
192 
251 
309 

367 

421 

483 

*023 
08  1 
I4O 
198 
256 

3'3 

373 
43i 
489 

*O29 

087 

146 

204 

262 
320 

379 
437 
495 

*035 
093 
IS* 

210 
268 
326 

384 
442 
500 

506 

512 

518 

523 

529 

535 

54i 

547 

SS2 

558 

N. 

L.  0    1 

234 

5 

6 

7 

8    9 

P.  P.    | 

S.'   TV 
7'  6.46373  373 
8     373  373 

0°  ] 
O  1 

S."  T." 
i'=  660"  4.68  557  558 

2  =  720     557  558 
3=  780      557  558 

i° 

2 

2 

59'=  7 
0  =  7 

S."  T." 
140"  4.68  549  575 
200     549  575 
260     549  575 
320     548  576 
380     548  576 
440     548  576 
500     548  577 

70     370  379 
71     37°  379 
72     369  379 
74     369  379 
75     369  380 

0  ] 

1  -7 

i  56  =  6960      549  574 
i  57  =  7020      549  574 
i  58  =  7080      549  575 
i  59  =  7140      549  575 

2    2-7 

2   3  =  7 
2   4  =  7 
2   5  =  7 

411 


N,   L,  0 

1    2    3 

4    5 

6    7  |  8  i  9 

P,  P, 

75O 

75  1 

752 
753 

754 
755 
756 

757 
758 
759 
760 
761 
762 
763 
764 

765 
766 

768 
769 
77O 

771 
772 
773 
774 
775 
776 

777 
778 
779 
78O 

781 
782 
783 
784 

7oO 

787 
788 
789 

79O 

791 

79  1 
793 
794 
795 
796 

797 
798 
799 
8OO 

87  506 

512 

518 

523 

529 

535 

541 

547 

552 

558 
616 
6/4 
731 

789 
846 
904 
961 
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076 

6 

i  j  0.6 

2  1.2 

3  1-8 
4  2.4 
5  3-0 
6  3.6 
7  4.2 
8  4.8 
9  5-4 

5 

i  0.5 

2   I.O 

3  1-5 
4  2.0 
5  2.5 
6  3-0 

7  3-5 
8  4.0 

9  4-5 

622 
679 

737 
795 
852 
910 

967 
88024 

570 
628 
685 

743 
800 
858 

915 
973 

576 
633 
691 

749 
806 
864 
921 
978 
036 

639 
697 

754 
812 
869 
927 
984 
041 

587 
045 
703 
760 
818 
875 

933 
990 
047 

593 
651 
708 

766 
823 
88  1 

938 
996 

053 

599 
656 

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40      557   55s 

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9  =77 

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oo      547  578 
60      547  579 
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40      546  579 

75      369  380 
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o  14  =  £ 

o  =78 
1=78 
2=79 
3  =79 
4=80 

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2   6=7560      548  577 
2   7=7620      548  577 
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2   I 
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2°  ] 
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8  =  82 

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2  15  =  8100      546  580 
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9-8. 

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22  =  8 

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121 
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275 
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131 
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136 
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331 
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091 
141 
191 

240 

290 
340 

389 
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047 

096 
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295 
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394 
443 

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453 

458 

463 

468 

473 

478 

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488 

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547 
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743 
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841 
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231 
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5°3 
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100 

148 
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153 

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299 

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1  68 
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S.'   T.' 
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1  9     373  373 

S."  T." 
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o  15  =  900      557   558 

2°  25'  =  87 
2  26  =87 

S."  T." 
oo"  4-68545  583 
60      544  584 
20      544  584 
80      544  584 
40      544  583 
oo      544  585 

85      368  381 
86      368   382 
89      368   382 
90      368  383 

2   21  =8460        545    582 
2  22  =8520        545   582 

2  23=8580      545  583 
2  24  =8640      545  583 
2  25  =8700      545   583 

2  28  =88 

2   29  =89 

2  30  =90 

414 


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P 

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10     373  373 

S."  T." 
o°  15'=  900-'  4.68  557  558 

o  16  =  960      557  558 

2°  34'  =92 

2  35  =  93 

S."  T." 
40"  4-68543  587 
oo      543  587 
60      543  587 
20      542  588 
80      542  588 
40      542  588 

90     368  383 
9i     368  383 
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94     367  383 
95     367  384 

2  30  =  9000      544  585 
2  31  =  9060      544  585 
2  32  =9120      543  586 
2  33  =  9i8o      543  586 
2  34  =  9240      543  587 

2  36-93 

2  37  =  94 
2  38  =  94 
2  39  =  95 

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5  |  6    7    8  |  9 

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9'  6.46  373   373 
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o°  15'=  c 
o  16  =  c 

S  "  T  " 
>oo"  4-68557  558 
60     557  558 
>20     557  558 

2°  4I'=  <> 

2  42  =  9 

S."  T." 
660"  4.68542  589 
720     541  590 
780      541  590 
840      541  590 
900      541  591 
960      541  591 

>020        540  592 

95     367  384 
98     367  384 
99     367   385 
100     366  385 

o  17  =  ic 

2  t 

\Z  -  9 

W  =  5 
t5  =  ^ 
16=  S 
\1  =ic 

2   38  =9480        542   588 

2  39  =9540      542  588 

2  40  =9600        542   589 
2  4I  =9660        542   589 

2  i 
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1 

2 

3 

4 

5 

6 

7 

8 

9 

S."   T."                      S."   T." 
2°  46'  =  9960"   4.68541    591     2°  51'  =  10260"   4.68540    593 
2  47  =  10020        540    592      2  52  =  10320        539    594 
2  48  =  10080       540    592     2  53  =  10380       539    594 
2  49  =  10140       540    592      2  54  =  10440       539    595 
2  50  =  10200       540    593     2  55  =  10500       539    595 

417 


N. 

L,   0 

1     2   |   3   |   4 

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N. 

L,   0 

1 

2 

3   !   4 

5 

6 

7 

8     9 

S."    T."                       S."    T." 
2°  55'  =  10500"   4-68539    595     3°o'  =  io8oo"    4-68538    597 
2  56  =  10560       539    595     3  i  =  10860        537    598 
2  57  =  10620       538    596     32=  10920        537    598 
2  58  =  10680       538    596     33=  10980        537    599 
2  59  =10740       538    597      3  4  =11040        537    599 

R  .M   L>    SL'KV.  2< 


418 


/ 

M, 

S'.  T', 

Sec. 

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24 

s 

3 

29 

30 

3i 
32 
33 
34 

Si 

11 

39 
4O 

4i 
42 
43 
44 
45 
46 

47 
48 

49 
5O 

5i 

52 
53 
54 

P 
11 

59 
60 

1  80 

6., 
353 

*6 
412 

10800 

4- 
538 

68 
597 

181 
182 
183 
184 
185 
186 
187 
1  88 
189 

353 
352 
352 
352 
352 
35i 
35i 
35  * 
351 

4i3 
413 
414 

414 
415 
415 

415 
416 
416 

10860 
10920 
10980 
11040 
moo 
11160 
1  1  220 
11280 
11340 

537 
537 
537 
537 
537 
536 

536 

53* 
536 

598 
598 
599 
599 
599 
600 

600 
60  1 
60  1 

190 

350 

417 

11400 

535 

602 

191 
192 
193 
194 

195 
196 

197 
198 
199 

350 
35° 
350 

350 
349 
349 
349 
349 
348 

417 
418 
418 
419 
419 
420 
420 
421 
421 

11460 
11520 
11580 
11640 
11700 
11760 
11820 
11880 
11940 

535 
535 
535 
534 
534 
534 
534 
533 
533 

602 
603 
603 
604 
604 
605 

605 
606 
606 

200 

348 

422 

I2OOO 

533 

607 

20  1 
202 
203 
204 
205 
206 
207 
208 
209 

348 
348 
347 
347 
347 
347 
346 
346 
346 

422 
423 
423 
424 
424 
425 

425 
426 
426 

I2O6O 
1  21  2O 
I2I80 
12240 
I23OO 
12360 
I242O 
12480 
12540 

533 
532 
532 
532 
S32 
53i 
53i 
53i 
53i 

607 
608 
608 
609 
609 
610 
610 
611 
611 

2IO 

346 

427 

12600 

530 

612 

211 
212 
213 

214 
215 

216 

217 

218 

219 

345 
345 
345 
343 
344 
344 
344 
344 
343 

427 
428 
428 
429 
429 
43° 
43° 
43i 
43i 

12660 
12720 
12780 
12840 
I29OO 
12960 
13020 
13080 
I3I40 

530 
530 
530 
529 
529 
529 

529 
528 
528 

612 
6^3 
613 
614 
614 
615 

615 
616 
616 

22O 

343 

432 

I32OO 

528 

617 

221 
222 
223 
224 
225 
226 
227 
228 
229 
"230" 

343 
342 
342 
342 
342 
341 
341 
341 
340 

432 
433 
434 
434 
435 
435 
436 
436 
437 

13260 
13320 
13380 

13440 
I3500 
13560 
13620 
13680 
13740 

528 
527 
527 

527 
526 

526 
526 
526 
525 

617 
618 
618 
619 
620 
620 
621 
621 
622 

340 

437 

13800 

525 

622 

231 

232 
233 
234 
235 
236 

237 
238 
239 

340 
340 
339 
339 

339 
338 

338 
338 
338 

438 
439 
439 
440 
440 
441 
441 
442 
443 

13860 
13920 
13980 
14040 
I4IOO 
14160 
I422O 
14280 
14340 

525 
525 
524 
524 
524 
523 
523 
523 
522 

623 
623 
624 
625 
625 
626 
626 
627 
628 

240 

337 

443 

14400 

522  |  628 

/ 

M, 

S', 

T'. 

Sec. 

S", 

T", 

O 

240 

6. 
337 

*6 
443 

14400 

4- 

522 

58 
628 

2 

3 

4 

1 

8 
9 

241 
242 
243 
244 
245 
246 

247 
248 

249 

337 
337 
336 

336 
336 
336 

335 
335 
335 

444 
444 
445 
446 
446 
447 

447 
448 
449 

14460 
14520 
14580 
14640 
14700 
14760 
14820 
14880 
14940 

522 
522 
521 

521 
521 
520 

520 
520 
520 

629 
629 
630 

631 
63i 
632 

632 
633 
634 

10 

250 

334 

449 

15000 

5i9 

634 

ii 

12 
13 
14 

:i 

J7 
18 

19 

25  * 
252 
253 
254 

255 
256 

257 
258 

259 

334 
334 
333 
333 
333 
332 

332 
332 
332 

45° 
45° 
45i 

452 
452 
453 
454 
454 
455 

15060 
15120 
15180 
15240 
15300 
15360 
15420 
15480 
15540 

519 
Si9 
518 

518 

518 
5^7 
517 
5J7 
516 

635 

& 

637 
637 
638 

638 
639 
640 

20 

260 

33i 

456 

15600 

516 

640 

21 
22 
23 
24 

2 

2 

29 

261 
262 
263 
264 
265 
266 
267 
268 
269 

33  i 
33i 
330 
330 
330 
329 
329 
329 
328 

456 
457 
457 
458 
459 
459 
460 
461 
461 

15660 
15720 
15780 
15840 
15900 
15960 
16020 
16080 
16140 

5i6 
5i5 

5i5 

5i3 

5H 
5H 
5H 
5i3 
5i3 

641 
642 
642 

643 
644 
644  . 

645 
646 
646 

30 

270 

328 

462 

16200 

5J3 

647 

3i 
32 
33 

34 

! 

38 

39 

271 

272 
273 

274 

275 
276 

277 
278 
279 

328 
327 
327 

327 
326 
326 
326 
325 
325 

463 
463 
464 

465 

465 
466 

467 
467 
468 

16260 
16320 
16380 
16440 
16500 
16560 
16620 
16680 
16740 

512 
512 

S" 

5" 
511 
5" 

5'o 
5io 
510 

648 
648 
649 
650 
650 
651 
652 
652 
653 

4O 

280 

32-5 

469 

16800 

5°9 

654 

4i 
42 

43 
44 

4£ 
46 

47 
48 

49 

281 

282 
283 
284 
285 
286 

287 
288 
289 

324 
324 
324 
323 
323 
323 
322 
322 
321 

469 

47° 
471 

472 
472 
473 
474 
474 
475 

16860 
16920 
16980 
17040 
17100 
17160 
17220 
17280 
17340 

5°9 
5°9 
508 

508 
508 
5°7 
5°7 
5°7 
506 

654 
655 
656 

656 

657 
658 

659 
659 
660 

50 

290 

321 

476 

17400 

506 

66  1 

5i 

52 
53 

54 

P 
P 

59 

291 
292 
293 
294 
295 
296 

297 
298 
299 

321 
320 
320 

320 
3i9 
3'9 

3*9 
3i8 
3i8 

477 
477 
478 

479 
479 
480 

481 
482 
482 

17460 
17520 
17580 
17640 
17700 
17760 
17820 
17880 
17940 

506 
505 
505 
503 
5°4 
5°4 
5°3 
503 
503 

66  1 
662 
663 
664 
664 
665 
666 
666 
667 

60 

300 

3J7 

483 

18000 

502 

668 

411) 


TABLE    XVI. 


THE    LOGARITHMS 


OF  THE 


TRIGONOMETRIC    FUNCTIONS 


FOR   EACH    MINUTE. 


Formulas  for  the  Use  of  the  Auxiliaries  S  and  T. 

1.    When  a  is  in  the  first  five  degrees  of  the  quadrant: 
log  sin  a  =  log  a'  -j-  S.'  log  a'    =  log  sin  a  +  cpl  5.' 


log  tan  a  =  log  a'  +  T.' 
log  cot  a  =  cpl  log  tan  a. 

log  sin  a  =  log  a"  -f  S." 
log  tan  a  =  log  a"  +  T.1' 
log  cot  a  =  cpl  log  tan  a. 


=  log  tan  a  +  cpl  T.' 

—  cpl  log  cot  a  4-  cpl  T: 

log  a"  =  log  sin  a  -f  cpl  5." 
=  log  tan  a  +  cpl  T." 
=  cpl  log  cot  a  +  cpl  T.'1 


2.    When  a  is  in  the  last  five  degrees  of  the  quadrant : 


log  cos  a  =  log(90°  —  a) '  -f  S.' 
log  cot  a  =  log(90°  —  a)'  -f  T.' 
log  tan  a  =  cpl  log  cot  a. 

log  cos  a  =  log(90°  -  a)"  -f  S." 
log  cot  a  =  log(90°  —  a)'7  -f  T." 
log  tan  a  =  cpl  log  cot  a. 

a  =  90° 


log(90°  — a)'  =  log  cos  a  +  cpl  S.1 
=  log  cot  a  +  cpl  T. ' 
=  cpl  log  tan  a  +  cpl  T.' 

log(90°- a) "=  log  cos  a  +  cpl  S." 
=  log  cot  a  +  cpl  T." 
=  cpl  log  tan  a  +  cpl  T." 

(90°  -  a). 


420 


0 


It 

/ 

L,  Sin, 

d. 

Cpl.  S', 

Cpl,  T', 

L,  Tan, 

c,  d, 

L,  Cot, 

L,  Cos, 

0 

O 

— 

— 

— 

— 

— 

o.ooooo 

6O 

60 

I2O 
1  80 
240 
300 
360 
420 
480 
540 

I 

2 

3 

4 

i 

9 

6.46  373 
6.76476 
6.94  085 
7.06579 
7.16270 
7.24  188 
7.30  882 
7.36  682 
7.41  797 

30103 

17609 
12494 
9691 
79i8 
6694 
5800 

5"5 

3-53627 

3-53  627 
3-53  627 
3-53  627 
3-53627 
3-53  627 
3-53  627 
3-53627 
3-53627 

3-53  627 
3-53627 
3-53  627 
3-53  627 
3-53627 
3-53627 

3-53  627 
3-53627 
3-53627 

646  373 
6.76476 
6.94085 
7.06579 
7.16  270 
7.24  188 
7.30  882 
7.36  682 
7.41  797 

30103 
17609 
12494 
9691 
7918 
6694 
5800 

5JI5 

3-53  627 
3-23  524 
3.05915 
2.93421 
2.8^?  730 
2.75812 
2.69  118 
2.63  318 
2.58  203 

o.oo  ooo 
o.oo  ooo 
o.oo  ooo 
o.oo  ooo 
o.oo  ooo 
o.oo  ooo 
o.oo  ooo 
o.oo  ooo 
o.oo  ooo 

59 

58 
57 
56 
55 
54 

53 
52 
51 

600 

IO 

746  373 

3-53  627 

3-53  627 

7-46  373 

2.53627 

o.oo  ooo 

5O 

660 
720 
780 
840 
900 
960 
IO2O 
I080 
1140 

ii 

12 
13 
H 
15 

16 

\l 

19 

7-50  512 
7.54291 

7-57767 
7.60  985 
7.63  982 
7.66784 
7.69417 
7.71  900 
7.74  248 

3779 
3476 
3218 
2997 
2802 
2633 
2483 
2348 

3-53  627 
3-53627 
3-53  627 
3-53  628 
3-53628 
3-53628 
3-53628 
3-53628 
3-53  628 

3-53627 
3-53627 
3-53  627 
3-53627 
3-53627 
3-53  627 
3-53627 
3-53627 
3-53627 

7-5°  512 
7.54291 

7-57767 
7.60  986 
7.63  982 
7-66  785 
7.69418 
7.71  900 
7-74  248 

3779 
3476 
3219 
2996 
2803 
2633 
2482 
2348 
2228 

2.49488 

2-45  7°9 
2.42  233 

2.39014 
2.36018 
2.33215 
2.30  582 
2.28  100 

2.25  752 

o.oo  ooo 
o.oo  ooo 
o.oo  ooo 
o.ooooo 
o.oo  ooo 
o.oo  ooo 

9-99  999 
9.99  999 

9-99  999 

49 
48 

47 
46 

45 
44 

43 
42 
4i 

1200 

20 

7-76475 

3-53  628 

3-53627 

7.76476 

2119 

2.23  524 

9-99  999 

4O 

1260 
1320 
1380 
1440 
1500 
1560 
l62O 
1680 
1740 

21 
22 
23 
24 

1 

27 
28 
29 

7-78  594 
7.80615 
7-82  545 

7-84  393 
7.86  166 
7.87  870 
7.89  509 
7.91  088 
7.92  612 

2021 
1930 
l848 

1773 
1704 
1639 

1579 
1524 

3.53628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 

3-53  627 
3-53627 
3-53627 

3-53  627 
3-53627 
3-53  627 
3-53626 
3.53626 
3-53  626 

778  595 
7.80615 
7.82  540 

7-84  394 
7.86  167 
7.87871 
7.89510 
7.91  089 
7.92613 

2O2O 

I931 
1848 

J773 
1704 
1639 

X579 
i524 
1473 

2.21  405 
2.19385 
2.17454 
2.15  606 

2.13833 
2.12  129 

2.IO49O 
2.O8  911 
2.07  387 

9-99  999 
9-99  999 
9.99  999 

9-99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  998 

39 
38 
37 
36 

35 
34 

33 
32 
3i 

I800 

30 

7-94  084 

3-53  628 

3-53  626 

7.94  086 

1424 

2.05  914 

9-99  998 

30 

1860 
1920 
1980 
2040 

2100 
2l6o 
222O 
2280 
2340 

31 

32 
33 

34 

H 

37 
38 
39 

7-95  5°8 
7.96  887 
7.98  223 
7.99  520 
8.00  779 

8.02  002 

8.03  192 
8.04  350 
8.05  478 

1379 
1336 
1297 

1259 
I223 
II9O 
1158 
1128 

3-53  628 
3-53  628 
3-53  628 
3-53628 
3-53628 
3-53628 
3.53628 
3.53628 
3.53  628 

3-53  626 
3-53  626 
3-53626 
3.53  626 
3.53626 
3-53  626 
3-53  626 
3-53626 
3.53  626 

7-95  510 
7.96  889 
7.98  225 

7-99522 
8.00  781 
8.  02  004 
803  194 

8-04  353 
8.05  481 

1379 
1336 
1297 

259 
223 
190 

159 
128 

2.04  490 
2.03  1  1  1 

2.01  775 

2.00  478 
1.99  219 
1.97996 
1.96806 
1.95647 
1.94519 

9-99  998 
9-99  998 
9-99  998 
9.99  998 
9-99  998 
9-99  998 
9-99  997 
9-99  997 
9-99  997 

29 
28 
27 
26 
25 
24 
23 

22 
21 

2400 

40 

8.06  578 

3-53  628 

3-53625 

8.06581 

072 

I.934I9 

9-99  997 

2O 

2460 
2520 
2580 
2640 
2700 
2760 
2820 
2880 
2940 

4i 

42 
43 
44 

3 

47 
48 
49 

8.07  650 
8.08  696 
8.09  718 
8.10717 
8.  1  1  693 
8.12647 
8.13581 
8.14495 
8.15  39i 

1046 
IO22 

999 
976 
954 
934 
914 
896 
877 

3.53  628 
3-53  628 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 

3-53  625 
3-53625 
3-53625 
3-53625 
3-53  625 
3-53  625 
3-53  625 
3-53  625 
3-53  624 

8.07  653 
8.08  700 
8.09  722 
8.10720 
8.  1  1  696 
8.12651 

8-13585 
8.14500 

8.15  395 

047 
022 
998 
976 

955 
934 

915 

895 

878 

L92347 
I.9I  300 
I.9O  278 
1.89280 
1.88304 
1.87349 
1.86415 
1.85  500 
1.84  605 

9-99  997 
9-99  997 
9-99  997 
9.99  996 
9-99  996 
9-99  996 
9-99  996 
9.99  996 
9.99  996 

19 

18 
J7 
16 
15 
H 
13 

12 
II 

3000 

50 

8.16268 

°/7 
860 

3-53  629 

3-53  624 

8.16273 

070 
860 

1.83727 

9.99  995 

IO 

3060 
3120 
3180 
3240 
3300 
3360 
3420 
3480 

354° 

51 

52 
53 
54 

11 

H 

59 

8.17  128 
8.17971 
8.18798 
8.19  610 
8.20407 
8.21  189 
8.21  958 
8.22713 
8.23456 

843 
827 
812 

797 
782 
769 

755 
743 

TiO 

3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  630 

3-53  624 
3-53  624 
3-53  624 
3-53  624 
3-53  624 
3-53  624 
3-53623 
3-53  623 
3-53  623 

8.I7I33 
8.17976 
8.18  804 
8.19616 
8.20413 
8.21  195 
8.21  964 

8.22  720 
8.23  462 

843 
828 
812 

797 
782 
769 

756 
742 

1.82867 
I.82O24 

1.81  196 
1.80384 
1.79587 
1.78805 
1.78036 
1.77280 
1.76538 

9.99  995 
9-99  995 
9-99  995 
9-99  995 
9-99  994 
9-99  994 
9-99  994 
9-99  994 
9-99  994 

9 

8 

7 
6 
5 
4 

3 

2 

3600 

60 

8.24  1  86 

/J^ 

3-53  630 

3-53  623 

8.24  192 

7JV 

1.75  808 

9-99  993 

0 

L,  Cos. 

d, 

L,  Cot, 

c.  d, 

L,  Tan, 

L,  Sin, 

/ 

89C 


421 


// 

I 

L.  Sin. 

d. 

Cpl.  S', 

Cpl.  T', 

L.  Tan. 

c.d. 

L.  Cot. 

L.  Cos. 

3600 

0 

8.24  1  86 

3-53  630 

3-53  623 

8.24  192 

-  i  x 

1.75808 

9-99  993 

60 

366o 
3720 
3780 
3840 
3900 
3960 
4020 
4080 
4140 

I 

2 

3 

4 

1 

9 

8.24  903 
8.25609 
8.26  304 
8.26  988 
8.27661 
8.28  324 
8.28977 
8.29  621 
8.30  255- 

717 
706 

695 
684 

673 
663 

653 
644 
634 

f\1A 

3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 

3-53  623 
3-53  623 
3-53  623 
3-53  622 
3-53622 
3.53622 

3-53  622 
3.53622 
3-53  622  ! 

8.24910 
8.25  616 
8.26312 
8.26  996 
8.27  669 
8.28  332 
8.28  986 
8.29  629 
8.30  263 

715 
706 
696 
684 

673 
663 

654 
643 
634 

f.~c 

1.75090 
1.74384 
1.73688 
1.73004 
1-72331 
1.71  668 

1.71  014 
1.70371 
1.69  737 

9-99  993 
9-99  993 
9-99  993 
9.99992 
9-99  992 
9-99  992 
9-99  992 
9-99  992 
9-99  991 

59 
58 
57 
56 
55 
54 

53 
52 
5i 

4200 

10 

8.30  879 

f.,f. 

3-53  630 

3-53621 

8.30  888 

025 
6lT 

1.69  112 

9-99  99i 

50 

4260 
4320 
4380 
4440 
45°° 
4560 

4620 
4680 
4740 

ii 

12 

U 
H 
15 
16 

17 
18 
19 

8.31  495 
8.32  103 
8.32  702 
8.33  292 
8-33  875 
8-34  45° 
8-35  018 
8-35  578 
8.36  131 

608 

599 
590 
583 
575 
568 
560 
553 

3-53  630 
3-53  631 
3'5363i 
3-5363I 
3-5363I 
3-5363I 
3-5363I 
3-5363I 
3-5363I 

3-5362I 
3-53  621 
3-53  621 
3-5362I 
3-53  620 
3-53  620 
3-53  620 
3-53  620 
3-53  620 

8-31  505 

8.32  112 
8.32711 

8-33  302 

8.33  886 
8.34461 
8.35  029 
8-35  590 
8.36  H3 

017 
607 

599 

59i 
584 

575 
568 

56i 
553 

C46 

1.68495 
1.67888 
1.67  289 
1.66698 

1.66  114 
I-65  539 
1.64971 
1.64410 
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31 

3 

64.8      64.2      63.9      63.3      62.7 

30 

8.78  568 

206 

8.78649 

2O6 

1.  21  351 

9.99919 

30 

4 
e 

86.4      85.6      85.2       84.4      83.6 

108.0  107.0  106.5  IO5-5  IO4-5 

31 

8.78  774 

8.78855 

1.21  145 

9.99918 

29 

6 

129.6  128.4  127.8  126.6  125.4 

33 

8.78979 
8.79  183 

204 

8.79061 
8.79  266 

205 

1.20939 

1.20  734 

9.99917 
9.99917 

28 
27 

7 

3 

9 

151.2  149.8  149.1   147.7   146.3 
172.8  171.2  170.4  168.8  167.2 
194.4  192.6  191.7  189.9  188.1 

34 

8-79  386 

3 

8.79  470 

4 

1.20530 

9.99916 

26 

35 

8-79  588 

8-79  673 

2O3 

1.20327 

9-999I5 

25 

208    206    203      2O1     199 

I  36 

8.79  789 

8-79  875 

i.  20  125 

9.99914 

24 

i 

20.8      20.6      20-3      20.1       19.9 

2O  I 

2O  I 

2 

41.6     41.2     40.6     40.2     39.8 

37 

8-79  990 

8.80076 

1.19924 

9-999I3 

23 

3 

62.4    61.8    60.9    60.3    59.7 

38 

8.80  189 

99 

8.80277 

1.19723 

9-999I3 

22 

4 

83.2    82.4    81.2    80.4    79.6 

39 

S.So  388 

199 

8.80  476 

199 
198 

1.19524 

9.99912 

21 

5 

n 

104.0  103.0  101.5  100.5     99.5 

40 

8.80  585 

97 

8.80  674 

198 

1.19  326 

9.99911 

20 

7 

145.6  144.2  142  I  140.7  139.3 

42 

8.80  782 
8.80  978 

196 

8.80  872 
8.81  068 

196 

1.19  128 
1.18932 

9.99910 
9-99  909 

19 
18 

S 

166.4  164.8  162.4  160.8   159-2 
187.2  185.4  182.7  180.9  179.1 

43 

S.Si  173 

*95 

8.8  1  264 

196 

1.18736 

9.99  909 

17 

198     196      194     192      19O 

44 

8.81  367 

194 

8.81  459 

19S 

1.18541 

9-99  908 

16 

i 

19.8     19.6     19.4     19.2     19.0 

8.81  560 

*93 

8.81  653 

194 

1.18347 

9-99  907 

IS 

2 

39.6     39.2     38.8     38.4     38-0 

40 

8.81  752 

192 

IQ2 

8.8  1  846 

193 

IQ2 

1.18  154 

9  99  906 

14 

3 

4 

59.4     58.8     58.2     57.6     57.0 
79.2     78.4     77.6     76.8     76.0 

47 
48 

49 

8.81  944 
8.82  134 
8.82  324 

190 
190 

i  So 

8.82  038 
8.82  230 
8.82  420 

192 
190 

1.17962 
1.17770 
1.17580 

9-99  905 
9-99  904 
9-99  904 

13 

12 
II 

5 
6 

I 

99.0    98.0    97.0     96.0    95.0 
118.8  117.6  116.4  115.2  114.0 
138.6  137.2  135.8  134-4  133.0 
158.4  156.8  155.2  153-6  152.0 

50 

8.82513 

ioy 
1  88 

8.82610 

1  80 

1.17390 

9-99  903 

10 

9 

178.2  176.4  174.6  172.8  171.0 

5i 
i  52 
53 

8.82  701 

8.82  888 
8.83075 

I87 
I87 

8.82  799 
8.82  987 
8-83  175 

188 

1  88 

I.I7  2OI 
I.I70I3 
1.16825 

9.99  902 
9-99  90i 
9-99  900 

9 

8 

7 

I 

2 

188     186      184     182       181 

18.8     18.6     18.4     18.2     18.1 
37.6    37.2    36.8    36.4    36.2 

54 

55 

56 

3 

8.83  261 
8.83446 
8.83  630 
8.83813 
8.83  996 

I85 
184 
I83 

I83 
T  of 

8.83  361 
8.83  547 
8.83  732 
8.83916 
8.84  loo 

186 

185 
184 
184 

1.16639 
1.16453 
I.I6268 
1.16084 
I.I5900 

9.99  899 
9-99  898 
9.99  898 

9.99  897 
9-99  896 

6 

5 
4 

3 

2 

3 
4 

5 
6 

I 

9 

56.4     55.8     55.2     54.6     54.3 
75-2     74-4     73-6     72-8     72.4 
94.0    93.0    92.0    91.0    90.5 
112.8  in.  6  110.4  109.2  108.6 
131.6  130.2  128.8  127.4  126.7 
150.4  148.8  147.2  145.6  144.8 
169.2  167.4  165.6  163.8  162.9 

59 

8.84  177 

181 

8.84  282 

182 

I.I5  718 

9.99  895 

I 

60 

8.84358 

8.84  464 

LI5536 

9.99  894 

0 

L,  Cos. 

d, 

L,  Cot. 

c,d, 

L.  Tan. 

L.  Sin. 

t 

P.  P. 

86' 


424 


' 

L.  Sin, 

d. 

L,  Tan, 

c,d, 

L,  Cot, 

L,  Cos, 

p,  p,              1 

o 

8.84358 

181 

8.84  464 

182 

I-I5536 

9-99  894 

60 

2 

3 
4 

| 

8.84  539 
8.84  718 
8.84897 
8.85075 
8.85  252 
8.85429 

179 
179 
178 
177 
177 

176 

8.84  646 
8.84  826 
8.85  006 
8.85  185 
8.85  363 
8.85  540 

1  80 
1  80 
179 
178 
177 

I-I5354 
1-15  J74 
1.14994 

1.14815 
1.14637 
1.14460 

9-99  893 
9.99  892 
9.99891 
9.99  891 
9-99  890 
9.99  889 

59 

58 
57 
56 
55 
54 

I 

2 

3 

4 

i 

182       181      180     179     178 

18.2     18.1     18.0    17.9     17.8 
36.4    36.2    36.0    35.8    35.6 
54-6     54-3     540     53.7     53.4 
72.8     72.4     72.0     71.6     71.2 
91.0    90.5     90.0     89.5     89.0 
109.2  108.6  108.0  107.4  106.8 

I 

8.85  605 
8.85  780 

l/U 

'75 

8.85  717 
8.85  893 

177 
176 

T76 

1.14283 
1.14  107 

9.99  888 
9-99  887 

53 

52 

7 
8 
9 

127.4  126.7  126.0  125.3  124.6 
145.6  144.8  144.0  143.2  142.4 
163.8  162.0  162.0  161.1  160.2 

9 

8-85  955 

173 

8.86069 

170 

1  74. 

I-I393I 

9.99  886 

51 

10 

8.86  128 

8.86  243 

1  74. 

I-I3757 

9-99  885 

5O 

177     176      175     174     173 

n 

8.86  301 

73 

8.86417 

1-13583 

9.99  884 

4Q 

I 

17.7     17  6     17.5     17.4     17.3 

12 
13 

8.86474 
8.86  645 

*73 
171 

8.86  591 
8.86  763 

172 

1.13409 
1-13237 

9-99  883 
9.99  882 

48 
47 

2 

3 
4 

35-4     35-2     35-o     34.8     34.6 
53.1     52.8     52.5     52.2     51.9 
70.8     70.4     70  o     69.6     69.2 

15 

8.86816 
8.86  987 

171 

171 

8.86935 
8.87  106 

172 
171 

1.13065 

1.  12  894 

9.99  881 
9.99  880 

46 

45 

7 

88.5     88.0    87.5     87.0     86.5 
106.2  105.6  105.0  104.4  103.8 

123.9    123.2    122-5    121.  8    121.  1 

16 

8.87  156 

tf\r\ 

8.87  277 

171 

1.12723 

9-99  879 

44 

8 

I4I.6    140.8    140.0    139.2    138.4 

18 
19 

8-87  325 
8.87  494 
8.87  661 

It>9 
I69 
I67 

1  68 

8.87  447 
8.87616 
8.87  785 

170 
169 
169 

1  68 

I-I2553 
1.12384 
I.I22I5 

9-99  879 
9-99  878 
9-99  877 

43 

42 

9 

T 

159.3  J58.4  !57-5  J56.6  155.7 

172      171      17O     169     168 
17.2     17.1     17  o     16.9     16.8 

20 

8.87  829 

166 

8.87953 

167 

I.I2O47 

9-99  876 

4O 

2 

34-4     34-2     34-o     33-8     33-6 

21 

22 

8.87  995 
8.88  161 

166 
i6c 

8.88  120 
8.88  287 

167 
1  66 

1.  1  1  880 
I.  II  713 

9-99  875 
9-99  874 

39 
38 

3 

4 

5x-6     5x-3     5I-o     50.7     50.4 
68.8     68.4     68.0    67.6    67.2 
86.0     85.5     850     84.5     84.0 

23 
24 

8.88  326 
8.88  490 

1D5 
164 

8.88453 
8.88618 

165 

L"  547 
i.  ii  382 

9-99  873 
9-99  872 

37 

36 

7 

103.2  102.6  102.0  101.4  100.8 
120.4  JI9-7  119-0  118.3  117-6 
137.6  136.8  136.0  135.2  134.4 

25 

8.88  654 

1  6 

8.88  783 

i6c 

i.  ii  217 

9.99871 

35 

9 

154.8  153.9  J53  °  I52-i  151.2 

26 

8.88817 

3 

8.88  948 

105 

1.11052 

9-99  870 

34 

27 
28 

8.88  980 
8.89  142 

162 
16? 

8.89  in 
8.89  274 

163 

1.10889 
i.io  726 

9.99  869 
9.99  868 

33 
32- 

i 

2 

167     166      165     164     163 

16.7     16.6     16.5     16.4    16.3 
33-4     33-2     33-o     32.8     32.6 

29 

8.89  304 

160 

8.89437 

161 

1.10563 

9-99  867 

31 

3 

50.1     49.8     49.5     49.2     48.9 

30 

8.89  464 

161 

8.89  598 

162 

1.10402 

9.99  866 

30 

4 
i? 

66.8    66.4    66.  o    65.6    65.2 
83.5     83.0    82.5     82.0    81.5 

31 

8.89  625 

I  CO 

8.89  760 

1  60 

i.io  240 

9-99  865 

2Q 

6 

100.2     99.6     99.0    98.4    97.8 

32 
33 

8.89  784 
8.89  943 

1  jy 
*59 

8.89  920 
8.90  080 

1  60 
1  60 

1.10080 
1.09  920 

9-99  864 
9-99  863 

28 
27 

9 

116.9  116.2  115.5  114.8  114.1 

133.6    132.8    132.0    131   2    130.4 

150.3  149.4  148.5  147.6  146.7 

34 

8.90  IO2 

8 

8.90  240 

1  .09  760 

9.99  862 

26 

35 

8.90  260 

8.90  399 

:59 

T  cX 

1.09  601 

9.99  861 

25 

v     162       161     16O      159     158 

36 

8.90417 

157 

8-90  557 

J55 

1.09443 

9.99  860 

24 

i 

16.2     16.1     16.0    15.9     15.8 

37 

8.90  574 

TC6 

8.90715 

:58 

1.09  285 

9-99  859 

2S 

2 

3 

32.4    32.2     32.0    31.8    31.6 
48.6     48.3     48  o    47.7     47.4 

38 

8.90  730 

J50 

8.90  872 

57 

1.09  128 

9-99  858 

22 

4 

64.8     64.4     64.0    63.6     63.2 

39 

8.90  885 

I  C  C 

8.91  029 

1^6 

1.08971 

9-99  857 

21 

i 

81.0    80.5     80.0     79.5     79.0 

40 

8.91  040 

T  CC 

8.91  155 

5 

1.08815 

9-99  856 

20 

113.4  112.7  112.  o  111.3  "0.6 

4i 
42 

8.91  195 
8.91  349 

1  JJ 

154 

8.91  340 
8.91  495 

'55 

1.08660 
i.  08  505 

9-99  855 
9-99  854 

19 
18 

9 

129.6  128.8  128.0  127.2  126.4 
145.8  144.9  I44-°  I43-1   J42.2 

43 

8.91  502 

53 

8.91  650 

55 

1.08350 

9-99853 

I7 

157     156      155     154     153 

44 

8.91  655 

53 

8.91  803 

J53 

i.  08  197 

9-99  852 

16 

T 

15.7     15.6     15.5     15.4     15.3 

8.91  807 
8.91  959 

152 

8.91  957 
8.92  no 

'53 

1.08043 
1.07  890 

9.99851 
9  99  850 

15 

2 

3 
4 

31.4     31.2     31.0     30.8     30.6 
47.1     46.8     46.5     46.2     45.9 
62.8     62.4     62.0     61.6     61.2 

47 

8.92  no 

ISl 

8.92  262 

*52 

1.07738 

9-99  848 

13 

5 

78.5     78.0     77.5     77.0     76.5 

48 
49 

8.92  261 
8.92411 

150 

I  CQ 

8.92414 
8.92  565 

152 

I  c  I 

1.07  586 
1-07435 

9-99  847 
9-99  846 

12 
II 

7 

94  2     93.6     93.0     92.4     91.8 

109.9    109  2    108.5    107.8    107.1 
125.6    124.8    124.0    123.2    122-4 

50 

8.92  561 

14.0 

8.92  716 

1.07284 

9-99  845 

IO 

9 

141.3    140.4    139.5    138.6    137.7 

53 

8.92  710 
8.92  859 
8.93  007 

149 
148 

8.92  866 
8.93016 
8-93  165 

150 

149 

1/18 

1.07  134 
1.06984 
1.06835 

9-99  844 
9-99  843 
9-99  842 

9 

8 

7 

2 

152      151      15O     149     148 

15.2     15.1     15.0     14  9     14.8 
30.4     30.2     30.0     29.8     29.6 

54 

55 

8-93  154 
8.93  301 

147 

8.93462 

140 
149 

1.06687 
1.06538 

9-99  841 
9.99  840 

6 

5 

3 
4 

5 

456     45.3     45-o     44-7     44-4 
60.8     60.4     60  o     59.6     59.2 
76.0     75.5     75.0     74.5     74.0 

56 

8.93  448 

J47 
_   /- 

8.93  609 

:47 

1.06391 

9-99  839 

4 

6 

91.2     90.6     90.0    89.4     88.8 

58 

8-93  594 
8.93  740 

146 

8.93  756 
8-93  903 

H7 

1.06244 
1.06097 

9-99  838 
9-99  837 

3 

2 

I 

9 

106  4  105.7  105.0  104.3  103.6 
121.  6  120.8  120.0  119.2  118.4 
136.8  135.9  135.0  134.1  133.2 

59 

8-93  885 

H5 

8.94  049 

146 

14.6 

i  -05  95  i 

9-99  836 

I 

160 

8.94  030 

8-94  195 

1.05  805 

9.99  834 

0 

L,  Cos.      d, 

L,  Cot, 

c,d, 

L,  Tan, 

L,  Sin, 

t 

P.  P, 

85' 


5° 


425 


1  ' 

L.  Sin, 

d. 

L.  Tan, 

c.d, 

L,  Cot, 

L,  Cos, 

P.  P, 

0 

8.94  030 

8.94  195 

1.05805 

9.99  834 

60 

2 

8-94  174 
8.94317 

144 
H3 

8-94  340 
8.94485 

*45 
'45 

1.05  660 
1-05  5'5 

9.99  833 
9.99  832 

59 

58 

147        146       145       144 

3 

8.94  461 

144 

8.94  630 

J45 

1.05370 

9.99831 

57 

2 

14.7       14  6       14.5       14.4 
29  4       29  2      29.0      28  8 

4 

5 

8.94  603 
8.94  746 
8.94  887 

143 
141 

8-94  773 
8.94917 
8.95  060 

*43 
144 

143 

1.05  227 
1.05  083 
1.04940 

9-99  830 
9-99  829 
9.99  828 

56 
55 
54 

3 

4 
5 
6 

44-1       43-8       43  5       43-2 
58.8       58.4       58.0       57.6 
735       730       725       720 
88.2       87.6      87.0      864 

8 
9 

8.95  029 
8.95  170 
8.95  310 

142 
141 

140 

IJ.O 

8.95  202 

8-95  344 
8.95  486 

142 
142 
142 

1.04798 
1.04656 
1.04514 

9-99  827 
9-99  825 
9.99  824 

53 
52 
51 

I 

9 

102.9       102.2       IOI-5       100.8 

117.6     116.8     116.0     115.2 
132.3     131.4     130.5     129.6 

IO 

8-95  45o 

8.95  627 

140 

1-04373 

9.99  823 

50 

143       142         141        14O 

1  1 

8.95  589 

I3y 

8.95  767 

1.04233 

9.99  822 

49 

i 

14  3       14.2       14.1       14.0 

12 
M 

8-95  728 
8-95  867 

M9 

8.95  908 
8.96  047 

141 
139 

1.04092 
1.03953 

9.99  821 
9.99  820 

48 
47 

3 

4 

42.9       42  6       42  3       42.0 
57.2       56.8       56.4       560 

14 
15 

8.96  005 
8.96  143 

138 

8.96  187 
8.96  325 

140 

138 

1.03813 
1.03673 

9.99819 
9.99817 

46 

45 

5 
6 
7 

71.5       71.0       70.5       70.0 
85.8       85.2       84  6       84.0 
100.  i       99.4       98.7       98.0 

16 

8.96  280 
8.96417 

137 

8.96  464 
8.96  602 

J39 
138 

1.03  536 
1.03398 

9.99  816 
9.99815 

44 

43 

8 
9 

114  4     113.6     112.  8     112.0 
128.7     127.8     126.9     126.0 

18 

8.96  553 

*3*j 

8.96  739 

1.03  261 

9.99814 

42 

139        138       137       136 

19 

8.96  689 

X^6 

8.96  877 

J3° 

1.03123 

9.99813 

41 

i 

13.9       13.8       13.7       13.6 

20 

8.96  823 

J 

8.97013 

3 

1.02  987 

9.99  812 

40 

2 

27.8       27.6       27.4       27.2 

21 
22 
23 

8.96  960 
8.97  093 
8.97  229 

135 
134 

8.97  130 
8.97  285 
8.97421 

'35 
136 

1.02850 
I.027I3 
1.02579 

9.99  810 
9.99809 
9.99  808 

39 
38 
37 

3 

55-6.       SS-2       54-8      54.4 
69.5      69  o      68.5       68.0 
83  4       82.8       82.2       81.6 
97-3      96.6      95  9      95.2 

24 

8-97  363 

Jj4 
133 

8-97  556 

!r 

1.02444 

9-99  807 

36 

8 

in.  2     110.4     109.6     108.8 

2^ 

8.97  496 

8.97  691 

o  o 

1.02309 

9.99  806 

35 

26 

8.97  629 

J33 

8.97  823 

*34 

1.02  175 

9.99  804 

34 

27 
28 

8.97  762 
8.97  894 

132 

8-97  959 
8.98  092 

A  34 
133 

I.0204I 

i.oi  908 

9.99  803 
9.99  802 

33 
32 

i 

2 

135        134        133       132 

*3-5       13-4       13-3       13-2 
27.0       26.8       26.6       26.4 

-9 

8.98  026 

132 

8.98  225 

133 

'•°i  775 

9.99  So  i 

3 

40.5       40.2       39.9       39.6 

30 

8.98  157 

1  j1 

8.98  358 

i.oi  642 

9.99800 

30 

4 

54-°       53-6       S3-2       52.8 
67.5       67.0       66  5       66.0 

31 

8.98  288 

I3l 

8.98  490 

J2 

i.oi  510 

9.99  798 

29 

6 

81.0      80.4       79  8      79-2 

32 

53 

8.98419 
8.98  549 

130 

8.98  622 
8.98  753 

132 

i.oi  378 
i.oi  247 

9.99  797 
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3.6  32.9  32.2 
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3.2  42.3  41.4 

45        44 

4-5       44 
9.0      8.8 

13-5     13-2 
18.0     17.6 

22.5       22.O 
27.0      26.4 
31.5       30.8 
36.0      35.2 
40.5      39.6 

4          3 

0.4      0.3 

0.8      0.6 

1.2         0.9 
1.6         1.2 
2.0         1.5 

2,4       1.8 

2.8         2.1 
3.2         2.4 
3.6         2.7 

9-4i  347 
941  394 
9.41  441 

9.41  488 

9-4i  535 
9.41  582 

9.41  628 
9.41  675 
9.41  722 

9.42  856 
9.42  906 
942957 
943  007 
943°57 
943  108 
943  158 
943  2°8 
943  258 

0.57  144 
0.57094 
0.57  °43 

0-56993 
0.50  943 
0.50892 
0.56  842 
0.56  792 
0.56  742 

9.98491 
9.98  488 
9.98484 
9.98  481 
9.98477 
9.98474 
9.98471 
9.98  467 
9.98  464 

9.41  768 

943  3°8 

0.56692 

9.98460 

9.41  815 
9.41  861 
9.41  908 

9-41  954 
9.42001 
9.42  047 
9.42  093 
9.42  140 
9.42  186 

943  358 
943  408 
943  458 
943  5°8 
943  558 
943607 

943  657 
943  7°7 
943  756 

0.56  642 
0.56  592 
0.56  542 
0.56492 
0.56  442 
0.56  393 
0-56  343 
0.56  293 
0.56  244 

9.98457 
9.98453 
9.98  450 

9.98  447 
9-98  443 
9.98  440 

9.98436 

9.98433 

9.98429 

9.42  232 

943  806 

0.56  194 

9.98  426 

9.42  278 
9.42  324 
9.42  370 
9.42416 
9.42  461 
9.42  507 

9-42  553 
9-42  599 
9.42  644 

943  855 
943  905 
943  954 
9.44004 
944053 
9.44  1  02 

9-44I51 

9.44  2OI 
9.44  250 

0.56  145 
0.56  095 
0.56  046 

0-55  996 
o-55  947 
0.55  898 

0-55  849 
0-55  799 
0-55  75° 

9.98422 
9.98419 
9.98415 
9.98412 
9.98  409 
9.98  405 
9.98  402 
9.98  398 
9-98  39! 

9.42  690 

944  299 

o-55  701 

9.98  391 

9-42  735 
9.42  781 
9.42  826 
9.42  872 
9.42917 
9.42  962 
9-43  o<38 
9-43  053 
9-43  098 

9-44  348 
9-44  397 
944  446 

944  493 
944  544 
944  592 
9.44  641 
944  690 
9-44  738 

0-55  652 
0-55  603 
0-55  554 
°-55  5°5 
0.55  456 
0.55  408 

o-55  359 
0.553JO 
0.55  262 

9.98  388 
9.98  384 
998381 

9.98377 
9.98  373 
9.98  370 

9.98  366 
9-98  363 
9.98  359 

9-43  H3 

944  787 

0-55213 

998356 

9-43  1  88 
9-43  233 
9-43  278 

9-43  323 
9-43  367 
9.43412 

9-43457 
9-43  5°2 
9.43  546 

944  836 
9.44  884 
9-44  933 
9.44981 
945  o29 
945  078 
9.45  126 
945  J74 
945  222 

0.55  164 
0.55  1  16 
0.55  067 

0-55  OI9 
0.54971 
0.54  922 
0.54  874 
0.54  826 
0.54  778 

9.98352 
9  98  349 
9.98  345 
9.98  342 
9-9^  338 
9-98  334 

9-98  33i 
9.98  327 
9.98  324 

4444 
50    49    48    47 

D    6.2    6.1    6.0   '5.9 
18.818.4  18.017.6 
,,31.2  30.6  30.0  29.4 
^43.842.942.041.1 

3333 
51     50    49    48 

°|  8.5    8.3    8.2    8.0 
\  25.5  25.0  24.5  24.0 
742.541.740.840.0 

9-43  59i 

945  271 

0.54  729 

9-98  320 

943  635 
943  680 
943  724 

943  769 
943813 
943  857 
943  901 
943  946 
943  990 

945  319 
945  367 
945  4i5 
945  463 
9455" 
945  559 
945  6o6 
945  654 
945  7°2 

0.54681 
0-54  633 
0-54  585 

0-54537 
0.54489 
0.54441 

0-54  394 
0.54  346 
0.54  298 

9-9831  7 
9-983I3 
9.98  309 
9.98  306 
9.98  302 
9.98  299 
9.98  295 
9.98  291 
9.98  288 

944  034 

945  75° 

0.54  250 

9.98  284 

L,  Cos.      d. 

L.  Cot.    c.  d.    L.  Tan. 

L.  Sin.       d. 

1 

P.P.                   1 

74' 


436 


16' 


/ 

L,  Sin, 

d, 

L,  Tan,    c,  d.     L.  Cot,  |   L,  Cos, 

d, 

p,  p. 

o 

9.44  034 

4.4. 

945  75° 

47 

0.54  250 

9.98  284 

60 

I 

2 

9.44078 

9.44  122 

44 

9-45  797 
945  84? 

.48 

0.54  203 

o-54  155 

9.98  281 
9.98  277 

4 

59 

58 

48     47      46 

.3 

9.44  1  66 

44 

945  892 

.0 

0.54  108 

9.98  273 

4 

57 

I 

4.8    4.7     4.6 

4 

I 

9.44  210 
944  253 
944  297 

44 
43 
44 

945  940 
945  987 
9.46  035 

45 

47 
48 

0.54  060 
0.54013 
0-53965 

9.98  270 
9.98  266 
9.98  262 

3 
4 
4 

56 

55 
54 

2 

3 

4 

9.6    9.4    9.2 
14.4  14.1   13.8 
19.2  1  8.8  18.4 

8 
9 

944  34i 
944  38? 
944  428 

44 
44 
43 

44 

9.46  082 
9.46  130 
946  177 

47 
48 

47 

47 

0.53918 
0.53  870 
o.53  823 

9.98  259 
9-98  255 
9.98251 

3 

4 
4 

53 
52 

6 
8 

24.0  23.5  23.0 
28.8  28.2  27.6 
33-6  32-9  32-2 
38.4  37.6  36.8 

IO 

944  472 

4.4. 

9.46  224 

47 

0.53  776 

9.98  248 

SO 

9 

43-2  42.3  41-4 

ii 

9.44516 

9.46271 

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0-53  729 

9.98  244 

49 

12 

944  559 

43 

9.46319 

4° 

0.53  68  1 

9.98  240 

4 

48 

45     44      43 

13 

9.44  602 

43 

9.46  366 

47 

0-53  634 

9.98  237 

3 

47 

15 

16 
17 

9.44  646 
9-44  689 
944  733 
944  776 

44 
43 
44 
43 

9.46413 
9.46  460 
9.46  507 

946  554 

47 
47 
47 
47 

0.53587 
0-53  540 
0-53  493 
0.53  446 

9-98  233 
9.98  229 
9.98  226 

9.98  222 

4 
4 
3 
4 

46 
45 
44 
43 

2 

3 
4 

s 

4.5     4.4    4.3 
9.0     8.8     8.6 
13.5  13.2  12.9 
18.0  17.6  17.2 

22.5    22.0    21.5 

18 
19 

9.44819 
9.44  862 

4.5 

43 

A_1 

9.46  60  1 
9.46  648 

4/ 

47 
46 

0-53  399 
0.53352 

9.98218 
9.98215 

4 
3 

42 

6 

7 

27.0    26.4    25.8 
31.5    30.8    30.1 

20 

944  905 

4.5 

9.46  694 

47 

0-53  306 

9.98  211 

4O 

8 

36.0    35.2    34.4 

21 

944  948 

43 

9.46  741 

0-53  259 

9.98  207 

39 

9 

40-5  39-6  38-7 

22 

944  992 

44 

9.46  788 

47 

0.53212 

9.98  2O4 

3 

38 

23 

945  °35 

43 

946835 

4/ 

0-53  165 

9.98  2OO 

4 

37 

42       41 

24 

945  077 

42 

9.46  88  1 

4 

0-53  "9 

9.98  196 

4 

36 

25 

945  I2° 

43 

9.46  928 

47 

0.53072 

9.98  192 

4 

35 

i 

84      8.2 

26 

945  163 

43 

AT. 

946  975 

47 
16 

0.53025 

9.98  189 

3 

34 

3 

12.6    12.3 

27 

9  45  206 

9.47021 

0.52979 

9.98  iS^ 

33 

4 

16.8    16.4 

28 

945  249 

43 

9.47  068 

47 

Aft 

0.52932 

9.98  181 

4 

32 

S 

2I.O     20.5 

29 

945  292 

43 

947  "4 

4° 
46 

0.52886 

9.98177 

4 

31 

6 

25.2     24.6 

3O 

945  334 

9.47  1  60 

47 

0.52  840 

9.98  174 

6 

30 

7 

29.4     28.7 

31 

32 

945  377 
945  4i9 

42 

947  207 
947  253 

46 

Aft 

0.52  793 
0.52  747 

9.98  170 
9.98  1  66 

4 

29 

28 

5 

9 

33-6     32.8 

37-8    36-9 

33 

945  462 

43 

947  299 

4° 

0.52  701 

9.98162 

27 

34 

945  5°4 

42 

947  346 

47 

Aft 

0.52  654 

9.98159  j    3 

26 

4           3 

35 
36 

945  547 
945  589 

43 

42 

947  392 
947  438 

4° 
46 
A(\ 

0.52608 
0.52  562 

9-98  155  ; 
9.98151 

25 
24 

i 

2 

0.4        0.3 
0.8        0.6 

37 

9.45  632 

43 

9-47  484 

46 

Aft 

0.52  516 

9.98  147 

4 

2^ 

3 

1.2          0.9 

38 

945  674 

42 

947  530 

4O 
Aft 

0.52  470 

9.98  144 

3 

22 

4 

1.6           1.2 

39 

945  7l6 

42 

947  576 

4U 

46 

0.52424 

9.98  140 

4 

21 

5 

2.O           1.5 

40 

945  758 

4.1 

9.47  622 

46 

0.52378 

9.98  136 

2O 

6 

2.4        1.8 

,,  o              0   _ 

42 
43 

945  80  1 
945  843 
945  885 

42 
42 

9.47  668 
947  7H 
947  76o 

46 
46 

Aft 

0.52332 
0.52  286 
0.52  240 

9.98  132 
9.98  129 
9.98  125 

3 

4 

19 

18 
17 

8 
9 

3.2      2.4 

3-6        2.7 

44 

4* 

4° 

4 

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45 

945  927 
945  969 

42 

y.4/  aw 

9  47  852 

46 

0.52  148 

9.98117 

4 

IS 

46 

9.46011 

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947  897 

45 

A  (\ 

0.52  103 

9.98113 

4 

14 

4 

444 

47 

48 

49 

9.46053 
9.46  095 
9.46  136 

42 
42 
41 
4.2 

947  943 
947  989 
948035 

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46 

4.C 

0.52057 
0.52011 
0.51965 

9.98  no 
9.98  106 
9.98  102 

3 
4 
4 

13 

12 
II 

48    47     46     45 

0    6.0    5.9    5.8    5.6 
18.0  17.6  17.2  16.9 

50 

9.46178 

4.2 

9.48  080 

46 

0.51  920 

9.98  098 

IO 

30.029.428.8  28.1 

51 

9.46  220 

9.48  126 

0.51  874 

9.98  094 

9 

342.041.140.239.4 

52 

9.46  262 

T 

9.48171 

45 

Aft 

0.51  829 

9.98  090 

4 

8 

53 

946  3°3 

41 

9.48217 

4° 

0.51  783 

9.98087 

3 

7 

3 

333 

54 

946  345 
9.46  386 

41 

9.48  262 
9.48  307 

45 

11 

0.51  738 
0.51  693 

9.98083 
9.98  079 

4 
4 

6 

S 

48 

47     46    45 

56 

9.46  428 

4Z 

948  353 

40 

0.51  647 

9.98  075 

4 

4 

0    8.0    7.8    7.7    7.5 

57 
58 

9.46  469 
9.46511 

41 
42 

9.48  398 
9.48  443 

4o 
45 

0.51  602 
o-S1  557 

9.98071 
9.98  067 

4 
4 

3 

2 

24.0  23.5  23.0  22.5 
3  40.0  39.2  38.3  37.5 

59 

946  552 

41 
42 

9.48  489 

4.C 

0.51  5" 

9.98  063 

4 

I 

60 

9.46  594 

948  534 

0.51  466 

9.98  060 

O 

L,  Cos.      d. 

L.  Cot,    |c.  d.     L.  Tan. 

L.  Sin.       d, 

t 

P,  P, 

73C 


17' 


437 


1 

L,  Sin, 

d. 

L.  Tan, 

c.  d,     L,  Cot, 

L,  Cos, 

d, 

P,  P, 

o 

946  594      „  T 

948  534 

AC 

0.51  466 

9.98  060 

4" 

60 

I 

946  635 

948  579 

0.51  421 

9.98  056 

S9 

2 

3 

946  676 
9.46717 

41 

4i 

948  624 
948  669 

45 
45 

0.51  376 
0-51  331 

9.98  052 
9.98  048 

4 
4 

58 
57 

45     44     43 

4 
6 

8 
9 

946  758 
9.46  800 
946841 
9.46  882 
946  923 
946  964 

41 

42 

4i 

A  I 

9.48  714 
948  759 
9.48  804 

9.48  849 
9.48  894 
9-48  939 

4S 

45 
45 
45 
45 
45 

AC 

0.51  286 
0.51  241 

0.51  196 

0.51  151 
0.51  106 
0.51  061 

9-98  044 
9.98  040 
9.98  036 
9.98  032 
9.98  029 
9.98025 

4 
4 
4 
4 
3 
4 

56 
55 
54 

53 
52 
51 

i 

2 

3 
4 

1 

7 

4-5    44    4-3 
9.0    8.8    8.6 
13.5  13.2  12.9 
18.0  17.6  17.2 

22.5    22.0   21.5 
27.0    26.4    25.8 
31.5    30.8    30.1 

IO 

947  005      ^0 

948  984 

AC 

0.51  016 

9.98021 

SO 

8 

36.0  35.2  344 

ii 

947  °45 

949029 

0.50971 

9.98017 

49 

9 

40.5  39-6  38-7 

12 

947086     J 

949  073 

44 

0.50927 

9.98013 

48 

13 

947  I27 

949  118 

45 

0.50  882 

9.98009 

47 

14 

947168     4 
947  209      T0 

949  l63 
949  207 

45 
44 

0.50837 
0.50  793 

9-98005 
9.98001 

46 
45 

42     41     40 

16 

947  249     T, 

949  252 

45 

0.50  748 

9-97  997 

44 

i 

4.2    4.1     4.0 

1  8 
19 
20 

9.47  290 
947  330 

947  37  i 

T"1 
40 

41 
40 

41 

949  296 
949  34i 
949  385 

44 
45 
44 
45 

AA 

0.50  704 
0.50  659 
0.50615 

9-97  993 
9-97  989 
9-97  986 

4 
4 
3 
4 

A 

43 

42 

40 

2 

3 
4 

6 

84    8.2    8.0 
12.6  12.3  12.0 
1  6.8  164  1  6.0 

2I.O   2O-5    2O.O 
25.2   24.6  24.0 

9.47411 

9-49  430 

0.50570 

9.97  982 

21 

947  452 

4O 

949  474 

AC 

0.50  526 

9.97978  1    ~[ 

39 

7 

29.4  28.7  28.0 

22 

947  492 

41 

949  5  19 

AA 

0.50481 

9-97  974 

38 

8 

33.6  32.8  32.0 

23 

947  533 

4O 

949  563 

AA 

0.50  437 

9-97  97° 

37 

9 

37-8  36.9  36-0 

24 

947  573 

9.49  607 

0.50  393 

9-97  966 

36 

25 

947613 

4U 

949652 

0.50  348 

9.97  962 

35 

26 

947  654 

949  696 

0.50  304 

9-97958 

34 

27 

947  694 

4° 

AO 

949  740 

44 

0.50  260 

9-97  954 

33 

39    5     4     3 

28 

29 

947  734 
947  774 

40 

4O 

949  784 
949  828 

44 
44 

0.50  216 
0.50  172 

9-97  95° 
9.97  946      ' 

32 

i 

2 

3.9  0.5  04  0.3 
7.8  i.o  0.8  0.6 

3O 

9.47814 

4O 

949  872 

AA 

0.50  128 

9-97  942 

30 

3 

11.7  1.5  1.2  0.9 

31 

947  854 

949  9i6 

0.50  084 

9-97  938 

29 

4 

15.6   2.O    1.6    1.2 

32 

9.47  894 

4° 

949  960 

44 

0.50  040 

9-97  934 

28 

5 

19.5    2.5    2.0    1.5 

33 

947  934 

4° 

9-5°  °°4 

44 

0.49  996 

9-97  930 

27 

b 

23.4  3.0  24  1.8 

34 

P 

947  974 
948014 
948  054 

40 
40 
40 

9.50  048 
9.50092 
9.50  136 

44 
44 

44 

049  952 
049  908 
0.49  864 

9.97  926 
9-97922 
9.97918      * 

26 
25 
24 

9 

27.3    3.5    2.8    2.1 

31.2  4.0  3.2  24 
35.1  4.5  3.6  2.7 

37 

948  094 

40 

9.50  180 

44 

049  820 

9.97914 

23 

38 

948  133 

j9 

9.50  223 

4j> 

°-49  777 

9.97  910 

22 

39 

9-4<S  173 

40 

AO 

9.50  267 

44 

A  A 

049  733 

9.97  906      ' 

21 

40 

948213 

9-50311 

AA 

049  689 

9.97  902 

t 

20 

41 

948  252 

j9 

9.5°  355 

049  645 

9-97  898 

4 

19 

544 

42 

9.48  292 

4 

9.50398 

4j 

049  602 

9.97  894 

18 

43     45      44 

43 

948  332 

40 

9.50442 

44 

049  558 

9.97  890 

17 

0 

44 
45 
46 

948371 
9.48411 
9.48  450 

39 
40 

39 

AO 

9.5°  485 
9-5°  529 
9-50572 

43 
44 

43 

049  51S 
0.49471 
049  428 

9.97  886 
9.97  882 
9-97  878 

4 
4 

A 

16 
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2 

3 

4-3     5-6    5-5 
12.9  16.9  16.5 
21.5  28.1  27.5 
30.1    394  38.5 

47 

9.48  490 

9.50616 

0.49  384 

9.97  874 

4 

13 

4 

38.7    —      — 

48 

948  529 

9oo659 

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049  34  * 

9  97  8/0 

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12 

5 

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948  568 

jy 

9-50703 

44 

A1 

0.49  297 

9.97  866 

4 

II 

5O 

948  607 

40 

9.50  746 

4"? 

0.49  254 

9.97  861 

IO 

5' 

948  647 

™ 

9.50  789 

0.49  211 

9-97  857 

9 

49             o 

52 

948  686 

9.5°  833 

44 

0.49  167 

9-97  853 

4 

8 

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948  725 

39 

9.50876 

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0.49  124 

9.97  849 

4 

7 

43     45      44 

54 

948  764 

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9.50919 

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0.49081 

9-97  845 

4 

6 

o 

54    7-5     7-3 

55 

9.48803 

39 

9.50  962 

43 

0.49  038 

9-97  841 

s 

1 

l6.I    22.5    22.O 

948  842 

39 

9.51005 

43 

048  995 

9-97  837 

4 

26.9  37-5  36.7 

57 

948  88  1 

39 

9.51  048 

43 

0.48  952 

9-97  833 

4 

3 

3 

37-6    -     — 

58 

9.48  920 

j9 

9.51092 

44 

0.48  908 

9-97  829 

4 

2 

59 

948  959 

39 

9-51  J35 

43 
4? 

048  865 

9.97  825 

4 

I 

60 

9.48998 

9.51  178 

0.48  822 

9.97  821 

O 

L,  Cos, 

d, 

L,  Cot,    c,  d.|   L,  Tan, 

L.  Sin, 

d. 

' 

P.  P, 

72° 


438 


18° 


; 

L.  Sin. 

d, 

L,  Tan, 

c,  d. 

L,  Cot. 

L.  Cos,       d, 

P.P. 

0 

948  998 

•JQ 

9.51  178 

47. 

048  822 

9.97  821 

6O 

I 

949  037 

9.51  221 

048  779 

9.97817 

59 

2 

3 

949  076 
9.49115 

39 
39 

9.51  264 
9.51  306 

43 
42 

0.48  736 
0.48  694 

9.97812 
9.97  808 

4 

58 
57 

43     42     41 

4 

I 

949153 
949  192 

949  231 

39 
39 

9-5  i  349 
9.51  392 

9-5  1  435 

43 
43 
43 
43 

048  65  1 
048  608 
048  565 

9-97  804 
9.97  800 
9.97  796 

4 
4 
4 
4 

56 
55 
54 

I 

2 

3 

4 

4-3     4-2     4-1 
8.6    8.4     8.2 
12.9  12.6  12.3 
17.2  16.8  16.4 

I 

9 

949  269 
9.49  308 
9-49  347 

39 
39 

78 

9-5  i  520 
9-5  *  563 

42 
43 

048  522 
0.48  480 
048  437 

9.97  792 
9-97  788 
9.97  784 

4 
4 

53 

52 

I 

7 

21-5    21.0    20-5 

25.8  25.2  24.6 

TO  I    2Q  4    28  7 

IO 

9-49  385 

0° 

•J.Q 

9.51  606 

42 

048  394 

9.97  779 

A 

50 

8 

34.4  33.6  32.8  ! 

ii 

949  424 

9.51  648 

0.48  352 

9-97  775 

49 

9 

38.7  37.8  36.9  1 

12 

9.49  462 

-jQ 

9.51  691 

43 

0.48  309 

9.97  771 

48 

«3 

949  500 

35 

9-5  *  734 

43 

048  266 

9.97  767 

47 

14 

9-49  539 

39 

9.51  776 

42 

0.48  224 

9-97  763 

4 

46 

15 

949  577 

3 

9.51819 

0.48  181 

9-97  759 

4 

45 

39     38     37  ! 

16 

9.49615 

3 

9.51  861 

4* 

0.48  139 

9-97  754 

44 

i 

3-9     3-8     3-7 

17 

9-49  654 

38 

9.51903 

4Z 

0.48  097 

9-97  75° 

43 

2 

7.8     7.6     74 

18 

9.49  692 

9.51946 

048  054 

9-97  746 

42 

3 

11.7  11.4  ii.  i 

19 

949  73° 

78 

9.51  988 

4* 

048012 

9-97  742 

4r 

4 

15.6  15.2  14.8 

2O 

949  768 

o° 

9.52031 

42 

047  969 

9-97  738 

4 

4O 

5 

19.5  19.0  18.5 

21 

22 
23 
24 

949  806 

949  844 
9.49  882 

9.49  920 

38 
38 
38 
78 

9.52073 
9.52115 
9-52  157 
9.52  200 

42 
42 

43 

A2 

047  927 
047  885 
047  843 
0.47  800 

9-97  734 
9.97  729 

9-97  725 
9.97  721 

5 
4 
4 

39 
38 
37 
36 

6 

8 
9 

23.4    22.8    22.2 
27.3    26.6    25.9 
31.2    304    29.6 
35.1    34.2    33.3 

2 

949  958 
949  996 

6° 
38 

9.52  242 
9.52  284 

42 

0.47  758 
047  716 

9.97717 
9-97  713 

4 

35 
34 

27 

28 

29 

9.50  034 
9.50072 
9.50  1  10 

38 
38 
78 

9.52326 
9.52  368 
9.52410 

42 
42 
42 

42 

047  674 
047  632 
0.47  590 

9-97  7°8 
9-97  7°4 
9-97  7°° 

5 
4 
4 

A 

33 
32 

i 

36       5       4 

3.6    0.5    04 

30 

9.50  148 

0° 

27 

9-52452 

42 

047  548 

9-97  696      1 

30 

10  8    1.5    1.2 

31 
32 
33 

9.50  185 
9.50  223 
9.50  261 

38 
38 

77 

9-52  494 
9.52  536 
9-52  578 

42 
42 
42 

047  506 
0.47  464 
047  422 

9.97691 
9-97  687 
9-97  683 

4 

4 

29 
28 
27 

4 
6 

144    2.0    1.6 
1  8.0    2.5    2.0 
21.6    3.0    2.4 

34 

9.50  298 

Jl 

78 

9.52  620 

41 

047  380 

9-97  679 

5" 

26 

7 

25.2    3.5    2.8 

35 

9-5°  336 

6° 

78 

9.52  661 

42 

047  339 

9.97  674 

4" 

25 

8 

28.8   4.0    3.2 

36 

9-5°  374 

6° 

9.52  703 

0.47  297 

9.97  670 

24 

9 

324  4.5  3.6 

37 

38 

9.50411 
9-50449 

37 
38 

27 

9-52  745 
9.52  787 

42 
42 

42 

047  255 
047  213 

9.97  666 
9.97  662 

4 

c 

23 

22 

39 

9.50  486 

27 

9.52  829 

4.1 

047  171 

9-97  657 

4 

21 

40 

9-5°  523 

9-52  870 

42 

0.47  130 

9-97653 

4 

20 

41 

9-5°  56i 

9.52912 

047  088 

9.97  649 

19 

555 

42 
43 

9-5°  598 
9.50635 

67 

37 

9.52953 
9.52995 

41 
42 

047  047 
047  °°5 

9-97  645 
9-97  64° 

5 

18 

17 

o 

43     42     41 

44 

i 

:  47 

I  48 

9.50  673 
9.50710 
9.5°  747 

9-5°  784 
9.50821 

37 
37 
37 
37 

9.53037 
9-53078 
9.53  120 

9-53  l6i 
9-53  202 

42 
41 

42 
41 
41 

046  963 
0.46  922 
046  880 
046  839 
046  798 

9-97  636 
9-97  632 
9.97  628 

9-97  623 
9-97619 

4 
4 
5 
4 

16 
15 

13 

12 

i 

2 

3 
4 

5 

4-3     4-2     4-1 
12.9  12.6  12.3 

21.5    2I.O    20.5 
30.1    29.4   28.7 

38-7  37-8  36-9 

49 

9.50858 

37 

•78 

9-53  244 

41 

0.46  756 

9.97615 

c 

II 

50 

.9-50  896     "„ 

9-53  285 

42 

0.46715 

9.97  610 

10 

9.50933 

o/ 

9-53  327 

0.46  673 

9.97  606 

9 

44        4 

52 
53 

9.50970 
9.51  007 

37 

37 

9-53  368 
9-53  409 

41 

41 

0.46  632 
046  591 

9.97  602 
9-97597 

5 

8 

7 

43      42     41 

1  54 
55 

9.51043 
9.51  080 

37 

9-5345° 
9-53492 

41 

42 

0.46  550 

046  508 

9-97  593 
9-97  589 

4 

4 

6 

5 

o 
i 

54    S-2     5-1 
16.1   15.8  154 

56 

9-51  "7 

37 

9-53533 

41 

0.46  467 

9-97  584 

4 

26.9  26.2  25.6 

57 

9.51  154 

37 

9.53  574 

41 

0.46  426 

9.97  580 

4 

3 

4 

37-6  36-8  35-9 

58 

9.51  191 

37 

9.53615 

41 

0.46  385 

9-97  576 

2 

59 

9.51  227 

77 

9.53656 

41 
4.1 

046  344 

9-97  571 

4 

I 

60 

9.51  264 

9.53697 

0.46  303 

9-97  567 

O 

L.  Cos, 

d, 

L.  Cot. 

c.  d,    L,  Tan. 

L,  Sin, 

d. 

1 

P,  P. 

19' 


439 


~T~ 

L.  Sin. 

d. 

L.  Tan. 

c.  d. 

L.  Cot. 

L.  Cos. 

d. 

P.  P. 

O 

9.51  264 

9-53697 

41 

0.46  303 

9-97567  ' 

60 

i 

9.51  301 

9-53  738 

0.46  262 

9-97  563 

59 

2 

3 

9-5  i  338 
9-51  374 

% 

11 

9-53  779 
9.53  820 

41 
41 

0.46  221 
0.46  1  80 

9-97  558 
9-97  554 

4 

58 

57 

41     40     39 

4 

i 

8 
9 

9.51411 
9-5  l  447 
9.51  484 

9.51  520 

9-5  i  593 

11 

36 

37 
36 

| 

9.53  861 
9-53  902 
9-53  943 

9-53  984 
9-54025 
9.54065 

41 
41 
41 
41 

41 
40 

41 

0.46  139 
0.46  098 
0.46057 
0.46016 

0-45  975 
o.45  935 

9-97  55° 
9-97  545 
9-97  54i 
9-97  536 
9-97  532 
9-97  528 

4 
5 
4 
5 
4 
4 

56 
55 
54 

53 
52 

3 
4 

6 

7 

4.1     4.0    3.9 
8.2     8.0     7.8 
12.3  12.0  1  1.  7 
16.4  16.0  15.6 

20.5    20.0    19.5 

24.6  24.0  23.4 

28.7  28.0  27.3 

10 

9,51  629 

77 

9-54  106 

41 

0.45  894 

9-97  523 

4 

SO 

8 

32.8  32.0  31.2 

ii 

9.51  666 

9-54  H7 

0-45  853 

9-975*9 

49 

9 

36.9  36.0  35.1 

12 

9.51  702 

3 

9-54  187 

41 

0.45813 

9-97  5'5 

4 

48 

13 

9-51  738 

if\ 

9-54  228 

o-45  772 

9.97510 

47 

14 

9-5  J  774 

3b 

9-54  269 

41 

4O 

0-45  73i 

9-97  5°6 

4 

46 

'5 

9.51  811 

3Z 

9-54  3°9 

0.45  691 

9-97  501 

45 

37      36      35 

16 

9.51  847 

">A 

9-54  35° 

4* 

0.45  650 

9-97  497 

4 

44 

i 

3-7     3-6     3-5 

17 
18 
19 

9.51  883 
9-5I9i9 
9-51  955 

3° 
36 
36 

9-54  390 
9-54431 
9-54  471 

4° 

41 
40 
41 

0.45  610 
o-45  569 
0-45  529 

9-97  492 
9.97488 
9-97  484 

5 
4 

4 
t 

43 
42 

2 

3 
4 

7-4     7-2     7-° 
11.  i   10.8  10.5 
14.8  14.4  14.0 

20 

9.51  991 

6 

9-545*2 

4O 

0.45  488 

9-97  479 

40 

5 
6 

22  2    21  6    21  O 

21 

22 

9-52027 
9.52063 

36 
16 

9.54552 
9-54  593 

41 
4O 

0.45  448 
0.45  407 

9-97  475 
9-97  47° 

5 

A 

39 
38 

8 

25.9    25.2    24.5 

29.6  28  8  28.0 

23 

9.52099 

9-54  633 

4O 

0.45  367 

9-97  466 

C 

37 

Q 

33-3  32-4  3*-5 

24 

9-52  135 

^ 

9-54673 

41 

0-45  327 

9-97  46i 

36 

25 

9.52171 

16 

9-54  7  H 

4° 

0.45  286 

9-97457 

4 

35 

26 

9.52  207 

9.54  754 

0.45  246 

9-97453 

34 

27 

9.52  242 

35 

9-54  794 

4° 

0.45  206 

9-97  448 

5 

33 

34     5      4 

28 

9-52  278 

76 

9.54835 

41 

A.O 

0.45  165 

9-97  444 

4 

32 

I 

3-4    0.5    0.4 

29 

9-52  3H 

ou 
^6 

9.54875 

4O 

0-45  *  25 

9-97  439 

31 

2 

6.8    1.0    0.8 

30 

9-52  35° 

7C 

9.549I5 

4O 

0.45  085 

9-97  435 

30 

3 

10.2    1.5     1.2 

31 

32 
33 
34 

9-52  385 
9.52421 

9-52456 
9-52492 

JJ 
36 

35 
36 

9-54955 
9-54995 
9-55035 
9-55  °75 

4o 
40 
40 
40 

0.45  045 
0.45  005 
0.44  965 
0.44  925 

9-97  430 
9-97  426 
9.97421 

9.97417 

4 

5 
4 
c 

29 
28 

27 
26 

4 
6 

8 

13.6    2.0    1.6 

17.0     2.5      2.0 
20.4      3-0      2.4 

23-8    3-5    2.8 
27.2    4.0    3.2 

3 

9-52527 
9-52  563 

36 

9-55  IJ5 
9-55  J55 

40 

0.44  885 
0.44  845 

9.97412 
9-97  408 

4 

25 
24 

9 

30.6    4.5    3.6 

37 

9-52  598 

35 
76 

9-55  195 

4° 

4O 

0.44805 

9-97  403 

5 

23 

38 

9.52  634 

0° 

0.44  765 

9-97  399 

22 

39 

9-52  669 

35 
16 

9-55275 

40 

4° 

0-44  725 

9-97  394 

i> 

21 

4O 

9-52  7°5 

•2C 

9-553I5 

1° 

0.44  685 

9-97  390 

c 

2O 

41 

9.52  740 

JJ 

9-55  355 

40 

0.44  645 

9.97  385 

19 

555 

42 

9-52  775 

D 

9-55  395 

0.44  605 

9.97  381 

18 

41      40      39 

43 

9.52811 

36 

9-55  434 

0.44  566 

9.97  376 

17 

o 

i 

44 

45 
46 

9.52  846 
9.52  881 
9.52916 

35 
35 

9-55  474 
9-55  5H 
9-55  554 

4U 
40 
40 

TO 

0.44  526 
0.44  486 
0.44  446 

9-97  372 
9-97  367 
9-97  363 

4 
5 

4 

16 
15 

i 

2 

3 

4.1     4.0     3.9 

12-3    12.0    II.7 
20.5    20.0    19.5 
28.7    28.O    27.3 

47 
48 

9-52  951 

9.52  986 

35 

7C 

9-55  593 
9-55  633 

40 

4° 

0.44  407 
0.44  367 

9-97  358 
9-97  353 

5 
4 

13 

12 

4 
5 

36.9    36.0    35.1 

49 

9.53021 

9-55  673 

2.Q 

0-44  327 

9-97  349 

r 

II 

50 

9-53056 

^6 

9-55  712 

40 

0.44  288 

9-97344 

IO 

51 

9-53092 

9-55  752 

70 

0.44  248 

9-97  340 

: 

9 

444 

52 
53 

9-53  126 
9-53  161 

35 

9-55  79i 
9.55831 

40 

0.44  209 
0.44169 

9-97  335 
9-97  331 

4 

8 
7 

41      40     39 

54 

9-53  196 

35 

7C 

9-55  870 

39 
40 

0.44  130 

9-97  326 

5 

6 

o 

5.1     5.0     4.9 

55 

9-5323I 

9-55910 

7Q 

0.44  090 

9-97  322 

5 

15.4  15.0  14.6 

56 

9-53  266 

03 

9-55  949 

6? 

0.44051 

9.973I7 

4 

25.6  25.0  24.4 

57 

9-53301 

35 

9-55  989 

4° 

O.44OII 

9.97312 

5 

7 

4 

35-9  35-o  34-1 

58 

9-53  336 

35 

9.56028 

39 

0-43  972 

9-97  308 

4 

2 

59 

9-53  37° 

7  = 

9.56067 

jy 
4° 

o-43  933 

9-97  3°3 

4 

I 

60 

9-53  405 

9-56  107 

0-43  893 

9-97  299 

0 

L.  Cos. 

d. 

L.  Cot. 

c.  d 

L.  Tan. 

L.  Sin. 

1  d. 

' 

P.  P. 

70' 


440 


20' 


/ 

L,  Sin. 

d, 

L,  Tan, 

c,  d, 

L,  Cot, 

L,  Cos,  j 

d, 

P.  P, 

0 

9-53  405 

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9-56  107 

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0-43  893 

9-97  299 

e 

6O 

I 

2 

3 
4 

I 

8 
9 

9-53  440 
9-53475 
9-53  5°9 
9-53544 
9-53578 
9-53613 
9-53  647 
9-53  682 
9-53  7l6 

JJ 

35 
34 
35 
34 
35 
34 
35 
34 

9.56  146 
9.56  185 
9.56  224 
9.56  264 

9-56  303 
9.56  342 

9.56  381 
9.56  420 

9-56459 

39 
39 
40 

39 
39 
39 
39 
39 

-JQ 

0.43  854 
0.43815 
0.43  776 

o-43  736 
0.43  697 
0.43  658 
0.43  619 
0.43  580 
0-43  54i 

9-97  294 
9-97  289 
9.97  285 

9.97  280 

9-97  276 
9.97271 

9.97  266 
9.97  262 
9-97  257 

5 
4 
5 
4 
5 
5 
4 
5 

59 

58 
57 
56 
55 
54 

53 
52 
5i 

i 

2 

3 
4 

6 

7 

40      39      38 

4-0     3-9     3-8 
8.0     7.8     7.6 

I2.O    11.7    II.4 

16.0  15.6  15.2 

2O.O    19.5    19.0 
24.0    23.4    22.8 
28.0   27.3    26.6 

10 

9.53751 

35 
•34 

9-56498 

jy 

-JQ 

0-43  502 

9-97  252 

50 

8 

32.0   31.2    30.4 

ii 

12 
13 

14 
15 

16 

J7 

18 

19 

9-53  785 
9.53819 

9-53  854 
9-53  888 
9-53922 
9-53957 

9.53991 
9.54025 

9-54059 

J4 

34 
35 
34 
34 
35 
34 
34 
34 

-JA 

9.56537 
9-56576 
9-56615 
9-56  654 
9-56693 
9.56  732 

9.56771 
9.56810 
9.56  849 

39 
39 
39 
39 
39 
39 
39 
39 
^8 

0-43  463 
0.43  424 

0.43  385 
0-43  346 
0-43  307 
0.43  268 

0.43  229 
0.43  190 
0.43  151 

9-97  248 
9-97  243 
9.97  238 

9-97  234 
9-97  229 
9-97  224 
9.97  220 

9-97  215 
9.97  210 

5 
5 
4 
5 
5 
4 
5 
5 

49 
48 

47 
46 
45 
44 

43 
42 
4i 

9 

2 

3 
4 

36.0   35.1    34.2 

37      35      34 

3-7     3-5     3-4 
7.4     7.0    6.8 

I  1.  1     IO-5    IO.2 
14.8    14.0    13.6 
18.5    17.5    17.0 

20 

9.54093 

j4 

9-56  887 

j° 

1Q 

0-43  "3 

9.97  206 

5" 

40 

6 

22.2    2I.O    2O.4 

21 

22 
23 
24 

3 

27 
28 
29 

9.54127 
9.54161 
9.54  195 
9.54  229 
9.54  263 
9.54  297 
9-54331 
9-54  365 
9-54  399 

o4 
34 
34 
34 
34 
34 
34 
34 
34 

9.56926 
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0-37  532 
0.37  496 
0.37461 
0.37  426 
o-37  39i 
0-37  355 
0.37  320 
0.37  285 
0.37  250 

9.96451 
9.96  445 
9.96  440 

9.96  435 
9-96429 
9.96  424 

9.96419 
9.96413 
9.96  408 

5 
5 
6 

5 
5 
6 

5 

9 

8 

7 
6 

5 
4 

3 

2 
I 

0 

2 

3 
4 

5 

555 
37   36  35 

3-7  3-6  3-5 
1  1.  1  10.8  10.5 
18.5  18.0  17.5 
25.9  25.2  24.5 
33-3  32-4  31-5 

6O 

9.59  188 

9-62  785 

JJ 

0.37  215 

9.96  403 

O 



L.  Cos. 

d. 

L.  Cot.  | 

c.  d. 

L.  Tan. 

L.  Sin. 

d. 

' 

P.  P. 

67° 


23' 


/ 

L,  Sin. 

d. 

L,  Tan. 

c.  d.  L.  Cot. 

L-Cos. 

|  d. 

p.  p. 

0 

I 

2 

3 
4 

6 

8 
9 
10 
ii 

12 
13 
14 

II 

J7 
18 

19 
20 

21 

22 
23 
24 
25 
26 

27 
28 
29 

30 

31 
32 
33 
34 

ll 

37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 

48 

49 
5O 

9.59  1  88 

30 
29 
30 
3<> 
29 
30 
30 
29 
30 
29 

30 
29 
30 

29 

30 
29 
29 

30 
29 

29 
30 
29 
29 
29 
29 
30 
29 
29 
29 
29 
29 

29 
29 

29 
29 
29 
29 

29 
29 
28 

29 

29 
29 
28 

29 
29 

29 
28 
29 
28 

9.62  785 

35 
35 
35 
36 
35 
35 
35 
35 
35 
34 

35 
35 
35 
35 
35 
35 
34 
35 
35 
35 
35 
34 
35 
35 
34 
35 
34 
35 
35 
34 
35 
34 
35 
34 
35 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
34 
34 
35 
34 
34 
34 
34 
34 
34 
34 
34 
34 

0.37215 

9.96  403 

6 

5 
1  5 
6 

i 

5 

6 

•  5 
6 

5 
5 
6 

6 

5 
6 

6 

5 

i 

5 
6 

5 
6 

u 

5 

6 

6 

5 

6 

5 
6 

1 

5 
6 

I 
6 

i 

5 
6 

1 

6 

I 

5 
6 
6 

5 
6 

60 

59 
58 
57 
56 

55 
54 

53 
52 
5i 
50 

49 
48 
47 
46 

45 

44 

43 
42 
4i 
40 
39 
38 
37 
36 
35 
34 

33 
32 
3i 
30 

29 
28 
27 
26 

25 

24 

23 

22 
21 

20 

19 

18 

17 

16 
15 
U 

13 

12 
II 

IO 

9 

8 

7 
6 

5 
4 

3 

2 

O 

I 

2 

3 
4 

I 

8 
9 

I 

2 

3 
4 

6 

8 
9 

i 

i 
i 

2 
2 
2 

3 

i 
i 
i 

2 
2 

2 

2 

3 
4 

1 

8 
' 

36   35   34 

3-6  3-5  3-4 
7.2  7.0  6.8 
0.8  10.5  10.2 
4.4  14.0  13.6 
8.0  17.5  17.0 
1.6  21.0  20.4 
5.2  24.5  23.8 
8.8  28.0  27.2 
2.4  31.5  30.6 

30  29  28 

3.0  2.9  2.8 
6.0  5.8  5.6 
9.0  8.7  8.4 

2.O  II.  6  II.  2 

5.0  14.5  14.0 

8.0  17.4  16.8 
i.o  20.3  19.6 

4.0  23.2  22.4 

7.0  26.1  25.2 

6    5 

0.6   0.5 

1.2    I.O 

1.8   1.5 

2.4    2.0 
3.0    2.5 

3-6   3-o 
4-2   3-5 
4.8   4.0 

5-4   4-5 

9.59218 
9-59  247 
9o9277 
9-59  3°7 
9-59  336 
9-59  366 
9-59  396 
9o9425 
9-59455 

9.62  820 
9.62  855 
9.62  890 
9.62  926 
9.62  961 
9.62  996 
9.63031 
9.63  066 
9.63  101 

0.37  1  80 

o-37  H5 
0.37  no 

0.37  074 

°-37  °39 
0.37  004 

0.36  969 

0-36  934 
0.36  899 

9.96  397 
9.96  392 
9.96  387 

9-96  381 
9.96  376 
9.96  370 
9.96  365 
9.96  360 
9-96  354 

9-59  4*4 
9-59  5  H 
9-59  543 
9-59  573 
9-59  602 
9.59  632 
9.59  661 

9-59  690 
9-59  720 
9-59  749 
9-59  77* 

9-63  135 

0.36  865 

9-96  349 

9.63  170 
9.63  205 
9-63  240 
9.63  275 
9.63  310 
9-63  345 

9-63  379 
9.63414 
9.63  449 

0.36  830 
0.36  795 
0.36  760 
0.36  725 
0.36  690 
0.36  655 
0.36  621 
0.36586 
0-36551 

9-96  343 
9-96  338 
9.96  333 
9.96  327 
9.96  322 
9.96316 
9.96311 
9.96  305 
9.96  300 

9.63  484 

0.36  516 

9.96  294 

9.59  808 
9-59  837 
9-59  866 

9-59  895 
9-59  924 
9-59954 

9-59  983 
9.60012 
9.60041 

9.63519 

9-63  553 
9.63  588 

9.63  623 
9.63  657 
9.63  692 
9.63  726 
9.63  761 
9.63  796 

0.36481 
0.36  447 
0.36412 

°-36  377 
0.36  343 
0.36  308 

0.36  274 
0.36  239 
0.36  204 

9.96  289 
9.96  284 
9.96  278 

9-96  273 
9.96  267 
9.96  262 
9.96  256 
9.96251 
9.96  245 

9.60  070 

9.63  830 

0.36  170 

9.96  240 

9.60099 
9.60  128 
9.60157 
9.60  1  86 
9.60215 
9.60244 
9.60  273 
9.60  302 
9-60331 

9.63  865 
9.63  899 
9-63  934 
9.63  968 
9.64  003 
9.64  037 
9.64072 
9.64  1  06 
9.64  140 

0-36  135 
0.36  101 
0.36  066 
0.36  032 
o-35  997 
o-35  963 
0.35  928 
0.35  894 
0.35  860 

9.96  234 
9.96  229 
9.96  223 
9.96  218 

9.96  212 
9.96  207 
9.96  201 
9.96  196 
9.96  190 

o 

2 

3 

4 

i 

c 

2 

3 
4 

5 

666 
36   35   34 

3.0  2.9  2.8 
9.0  8.8  8.5 
15.0  14.6  14.2 

2I.O  2O-4  i 
27.0  26.2  25.5 
33.0  32.1  31.2 

5    5 
35   34 

3-5   3-4 

IO.5   10.2 
I7.5   I7.0 
24-5   23.8 
31.5   30.6 

9.60  359 

9-64I75 

0.35  825 

9.96  185 

9.60388  . 
9.60417 

9.60  446 
9.60  474 
9.60  503 
9.60532  . 
9.60561 
9.60589 
9.60618  , 
9.60  646  | 

9.64  209 
9.64  243 
9.64  278 
9.64312 
9-64  346 
9.64  381 

9.64415 
9.64  449 
9.64  483 

°-35  79i 
°-35  757 
0.35  722 

0.35  688 

0-35  654 
0.35  619 

°-35  585 
o-3555i 
o-35  5*7 

9.96  179 
9.96  174 

9.96  1  68 
9.96  162 
9.96  157 
9.96151 
9.96  146 
9.96  140 
9-96  135 

29 
29 

28 

29 
28 
29 
28 

29 
28 
28 

9.64517 

0-35  483 

9.96  12  i 

5i 

52 
53 
54 

3 

GO 

9.60675  I 
9.60  704 
9.60  732 
9.60761 
9.60  789 
9.60818 
9.60  846 
9-6o  875 
9.60  903 

9-64  552 
9.64  586 
9.64  620 
9.64  654 
9.64  688 
9.64  722 
9.64  756 
9.64  790 
9.64  824 

0.35  44* 
0.354U 
0.35  380 

0.35  346 
o.353i2 
o-35  278 
0.35  244 
0.35  210 
0-35  176 

9.96  123 

9.96  118 

9.96  112 

9.96  107 
9.96  ioi 

9.96095 

9.96090 
9.96  084 

9-96079 
9.96  073 

9.60931  , 

9.64858 

0.35  142 

L,  Cos. 

d.   L.  Cot. 

c.  d.  L.  Tan. 

L.  Sin. 

d.   ' 

P.  P. 

66' 


444 


24' 


/• 

L.  Sin. 

d. 

L,  Tan, 

c.  d. 

L,  Cot, 

L,  Cos, 

d, 

P.P. 

0 

I 

2 

3 
4 

6 

1 

9 
10 

ii 

12 
13 
H 
15 

16 
17 
18 
19 
20 

21 
22 
23 
24 

25 
26 

2 

29 
3O 

3i 

32 
33 
34 

35 
36 

3 

39 
4O 

4i 
42 

43 
44 

45 
46 

47 
48 

49 
50 

51 

52 
53 
54 
55 
56 

57 
58 
59 
6O 

9.60931 

29 
28 
28 
29 
28 
28 
28 

29 

28 
28 
28 
28 
28 
28 
28 
28 

29 

27 
28 
28 
28 
28 
28 
28 
28 
28 

27 

28 
28 
28 
27 
28 
28 
27 
28 
28 

27 

28 
27 
28 
27 
28 
27 
28 
27 
28 

27 
27 
28 
27 
27 
27 
28 
27 
27 
27 
27 
28 
27 
27 

9.64  858 

34 
34 
34 
34 
34 
34 
34 
34 
34 
33 
34 
34 
34 
34 
33 
34 
34 
33 
34 
34 
33 
34 
34 
33 
34 
33 
34 
33 
34 
33 
34 
33 
34 
33 
34 
33 
"33 
34 
33 
33 
34 
33 
33 
33 
34 
33 
33 
33 
33 
34 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 

0.35  142 

9.96  073 

6 

6 
6 

5 
6 
6 

5 
6 
6 

5 
6 
6 
6 

5 
6 
6 
5 
6 
6 
6 

5 
6 
6 

5 
6 
6 
6 

5 
6 
6 
6 
6 

5 
6 
6 
6 
6 

5 
6 
6 
6 
6 

6 
6 
6 
6 
6 

i 

6 
6 
6 
6 
6 
6 
5 

60 

59 
58 
57 
56 

55 
54 

53 
52 
51 
5O 

49 
48 
47 
46 
45 
44 

43 
42 
4i 
4O 

11 

37 
36 
35 
34 

33 
32 
3i 
3O 

29 
28 
27 
26 

25 
24 

23 

22 
21 

20 

19 
18 

17 
16 
15 
H 

".3 

12 
II 

10 

9 
8 

7 
6 
5 
4 

3 

2 

o 

34   33 

i   3-4   3-3 
2   6.8   6.6 
3  10.2   9.9 
4  13-6   13-2 
5  17.0  16.5 
6  20.4  19.8 
7  23.8  23.1 
8  27.2  26.4 
9  30.6  29.7 

29  28  27 

i   2.9  2.8  2.7 

2    5.8   5.6   5.4 

3   8.7  8.4  8.1 
4  ii.  6  ii.  2  10.8 
5  14.5  14.0  13.5 
6  17.4  16.8  16.2 
7  20.3  19.6  18.9 
8  23.2  22.4  21.6 
9  26.1  25.2  24.3 

6    5 

i  0.6   0.5 

2   1.2    I.O 

3  1.8   1.5 

4  2.4   2.0 
5  3-°   2.5 
6  3.6   3.0 
7  4-2   3-5 
8  4.8   4.0 

9  5-4   4-5 

9.60  960 
9.60  988 
9.61  016 
9.61  045 
9.61  073 
9.61  101 
9.61  129 
9.61  158 
9.61  1  86 

9.64  892 
9.64  926 
9.64  960 
9.64  994 
9.65  028 
9.65  062 
9.65  096 
9.65  130 
9.65  164 

0.35  108 
0.35  074 
0.35  040 
0.35  006 
0.34972 
o-34  938 
0.34  904 
0.34  870 
0.34  836 

9.96  067 
9.96  062 
9.96056 
9.96050 
9.96045 
9.96039 
9.96  034 
9.96  028 
9.96  022 

9.61  214 

9.65  197 

0.34  803 

9.96017 

9.61  242 
9.61  270 
9.61  298 
9.61  326 
9-6i  354 
9.61  382 

9.61411 

9.61  438 
9.61  466 

9.65  231 
9.65  265 
9.65  299 

9-65  333 
9.65  366 
9.65  400 

9-65  434 
9.65  467 
9.65  501 

0.34  769 

0-34  735 
0.34  701 

0.34  667 

o.34  634 
0.34600 

0.34  566 

o-34  533 
0.34  499 

9.96011 
9.96  005 
9.96000 

9-95  994 
9.95  988 

9-95  982 
9-95  977 
9-95  971 
9-95  965 

9.61  494 

9-65  535 

0-34  465 

9.95  960 

9.61  522 
9.61  550 
9.61  578 
9.61  606 
9.61  634 
9.61  662 
9.61  689 
9.61  717 
9.61  745 

9.65  568 
9.65  602 
9.65  636 
9.65  669 

9-65  7°3 
9.65  736 

9.65  770 
9.65  803 
9-65  837 

0-34  432 
0-34  398 
o-34  364 

0-34331 
0.34  297 
0.34  264 
0.34  230 
0.34  197 
0.34  163 

9-95  954 
9-95  948 
9-95  942 
9-95  937 
9-95  931 
9-95  925 
9-95  920 
9.95914 
9.95  908 

9.61  773 

9.65  870 

0.34  130 

9-95  902 

9.61  800 
9.61  828 
9.61  856 
9.61  883 
9.61  911 
9.61  939 
9.61  966 
9.61  994 

9.62  O2I 

9.65  904 

9-65  937 
9.65971 

9.66  004 
9.66038 
9.66071 
9.66  104* 
9.66  138 
9.66  171 

0.34  096 
0.34  063 
0.34029 

0-33  996 
0.33  962 
0.33  929 
0.33  896 
0.33  862 
0.33  829 

9-95  897 
9.95  891 

9-95  885 
9-95  879 
9-95  873 
9-95  868 
9.95  862 
9-95  856 
9-95  850 

9.62  049 

9.66  204 

0-33  796 

9-95  844 

9.62  076 
9.62  IO4 
9.62  131 
9.62  159 

9.62  1  86 
9.62  214 
9.62  241 
9.62  268 
9.62  296 

9.66  238 
9.66  271 
9.66  304 
9-66  337 
9.66371 
9.66  404 
9.66  437 
9.66  470 
9.66  503 

0.33  762 

o-33  729 
0.33  696 

0.33  663 
0.33  629 
o-33  596 
0-33  563 
o-33  530 
0-33  497 

9-95  839 
9^95  833 
9-95  827 
9.95821 

9-95  815 
9.95  810 

9-95  804 
9-95  798 
9-95  792 

665 
34  33  34 

?   2.8  2.8  3.4 

1    8.5   8.2  10.2 

;  14.2  13.8  17.0 
1  19.8  19.2  23.8 

4  25.5  24.8  30.6 

g  31.2  30.2  — 

9.62  323 

9-66  537 

o-33  463 

9.95  786 

9.62  350 
9.62  377 
9.62  405 
9.62  432 
9.62459 
9.62  486 
9.62513 
9.62  541 
9.62  568 

9.66  570 
9.66  603 
9.66  636 
9.66  669 
9.66  702 
9-66  735 
9.66  768 
9.66  80  1 
9.66  834 

0-33  430 
0-33  397 
0-33  364 

0.33331 
0.33  298 
0-33  265 
0.33  232 

0-33  199 
0.33  166 

9-95  78o 
9-95  775 
9-95  769 
9-95  763 
9-95  757 
9-95  751 
9-95  745 
9-95  739 
9-95  733 

9-62  595 

9.66  867 

0-33  133 

9.95  728 



L,  Cos, 

d. 

L,  Cot. 

c,  d. 

L,  Tan, 

L.  Sin, 

d. 

r 

p,  p, 

65' 


25° 


445 


1 

L.  Bm. 

d, 

L,  Tan, 

c.  d. 

L,  Cot. 

L,  Cos, 

d, 

P.  P. 

0 

9.62  505 

27 

9.66  867 

27 

0.33  133 

9-95  728 

6 

6O 

I 

2 

3 

4 

8 
9 

9.62  622 
9.62  649 
9.62  676 
9.62  703 
9.62  730 
9.62  757 
9.62  784 
9.62  8n 
9.62838 

27 
27 

27 
27 

27 

9.66  900 
9-66  933 
9.66  966 

9-66  999 
9.67032 
9.67  065 
9.67  098 
9.67  131 
9-67  163 

33 
33 
33 
33 
33 
33 
33 
o2 

0.33  100 
0.33067 
0.33034 
0.33001 
0.32  968 
0.32935 
0.32  902 
0.32  869 
0.32  837 

9-95  722 
9.95  716 
9.95  710 

9-95  7°4 
9-95  698 
9-95  692 
9-95  686 
9.95  680 
9-95  674 

6 
6 
6 
6 
6 

6 
6 

59 

57 
56 
55 
54 

53 
52 
5i 

I 

2 

4 
5 

33        32 

3-3      3-2 
6.6      6.4 
9-9       9-6 
13.2     12.8 
16.5     16.0 

to 

9.62  865 

27 

9.67  196 

T? 

0.32  804 

9.95  668 

5O 

6 

19.8     19.2 

ii 

12 
13 

"4 

IS 

16 

18 
19 

9.62  892 
9.62918 
9.62  945 
9.62972 
9.62  999 
9.63  026 
9.63052 
9.63079 
9.63  106 

27 
27 
27 
27 
26 

27 
27 

9.67  229 
9.67  262 
9-67  293 
9-67  327 
9-67  360 
9-67  393 
9.67  426 
9.67458 
9.67491 

33 
33 
32 

33 

33 

32 

1  1 

0.32771 
0-32  738 
0.32  705 

0.32  673 
0.32  640 
0.32  607 

0.32  574 
0.32  542 
0.32  509 

9-95  663 
9-95  657 
9-95651 

9.95  645 
9-95  639 
9-95  633 
9.95  627 
9.95  621 
9.95615 

6 

6 

6 

6 

6 

49 
48 
47 
46 
45 
44 

43 
42 
4i 

8 
9 

2 

23.1     22.4 
26.4     25.6 
29.7     28.8 

27        26 

2.7       2.6 

c  A          c  2 

20 

9-63  133 

*/ 

26 

9.67  524 

0.32476 

9.95  609 

6 

40 

3 

8.1       7.8 

21 

22 
23 
24 
25 
26 

27 
28 
29 

9-63  159 
9.63  1  86 

9-63213 
9.63  239 
9.63  266 
9-63  292 
9-63  3*9 
9-63  345 
9-63  372 

27 

26 

26 

9-67  556 
9.67  589 
9.67  622 

9-67  654 
9.67  687 
9.67  719 
9.67  752 

9-67  785 
9.67817 

33 

32 
33 
32 
33 

77 

0.32  444 
0.32411 
0.32  378 

0.32  346 

0.32313 
0.32  281 

0.32  248 
0.32215 
0.32  183 

9.95  603 
9-95  597 
9-95  59i 
9-95  585 
9-95  579 
9-95  573 
9-95  567 
9-95  56i 
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6 

6 

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6 

6 
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39 
38 
37 
36 
35 
34 

33 
32 

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8 
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10.8     10.4 

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16.2     15.6 
18.9     18.2 

21.6      2O.8 

24.3   23.4 

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9-63  398 

27 

9.67  850 

12 

0.32  150 

9-95  549 

6 

30 

765 

31 
32 
33 

34 
35 
36 

37 
38 
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9-63  425 
9.63451 
9.63  478 
9.63  504 
9-63  531 

9-63  583 
9.63610 
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27 

27 
26 

26 

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9.67  882 
9.67915 
9.67  947 
9.67  980 
9.68012 
9.68  044 
9.68077 
9.68  109 
9.68  142 

32 

32 

33 

0.32  118 
0.32  085 
0.32053 
0.32  020 
0.31  988 
0.31  956 
0.31  923 
0.31  891 
0.31  858 

9-95  543 
9-95  537 
9-95  531 

9-95  525 
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9-95  5°7 
9-95  5°° 
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6 
6 
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6 
6 
6 

6 
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29 
28 

27 
26 

25 
24 

23 

22 
21 

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2 

3 
4 

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9 

0.7     0.6    0.5 

1.4       1.2       1.0 

2.1     1.8     1.5 

2.8      2.4      2.O 

3-5     3-o    2.5 
4.2     3.6    3.0 
4-9    4-2    3-5 
5.6    4.8    4.0 

6-3     5-4    4-5 

4O 

9.63  662 

27 

9.68  174 

12 

0.31  826 

9-95  488 

6 

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9.63  689 
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9.68  206 
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26 

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9.68  336 
9.68  368 
9.68  400 
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0.31  697 
0.31  664 
0.31  632 
0.31  600 

0.31  568 
0.31  535 

9-95  464 
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0.31  503 

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9.64  002 
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9.64  132 
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26 
26 
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9-68  529 
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9-68  593 
9.68  626 
9.68  658 
9.68  690 
9.68  722 
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32 

32 

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32 
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32 
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0.31  471 
0.31  439 
0.31  407 

0-31  374 
0.31  342 
0.31  310 
0.31  278 
0.31  246 
0.31  214 

9-95  42i 
9-954*5 
9-95  409 
9-95  403 
9-95  397 
9-95  39* 
9-95  384 
9-95  378 
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6 
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9.64  184 

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9-95  366 

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9.64  184 

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9-64  365 
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9.68  850 
9.68  882 
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9-95  36o 
9-95  354 
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9-95  335 
9-95  329 
9-95  323 
9.95317 
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9-69  234 
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0.30  830 
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0.30  734 
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9.95  286 

9-95  279 
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25 
26 

25 
26 

25 
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25 
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9.69  488 
9.69  520 
9.69  552 
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9.69  679 
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32 
32 
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0.30  512 
0.30  480 
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9.95  236 
9.95  229 
9-95  223 
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39 
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9-64  953 

9.69  774 

31 

0.30  226 

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32 
33 
34 
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si 

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9.64  978 
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9-65  155 
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25 
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9.69  805 
9.69  837 
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0.30  163 
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9-95  '35 
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27 
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3  2.1   1.8 

4  2.8   2.4 

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9.65  205 

25 

9.70  089 

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9-65  255 
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9.66  221 
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9.66  270 
9.66  295 
9.66  319 

9-66  343 
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25 
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9.71  370 
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0.28  630 
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9.71  679 
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30 
31 
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31 
3i 
3° 
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0.28321 
0.28  291 
0.28  260 
0.28  229 
0.28  198 
0.28  167 
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9.94  786 
9-94  780 
9-94  773 
9-94  767 
9-94  760 
9-94  753 
9.94  747 
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28 
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9.66  682 

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9.66  706 
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9-oo  755 
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24 
24 
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9.72048 
9.72078 
9.72  109 
9.72  140 
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31 
30 
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31 

0.27  952 
0.27  922 
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0.27  860 
0.27  830 
0.27  799 
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9-94  7°7 
9.94  700 
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9-94  674 
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6 
7 
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9.66922 

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2.1   2.6   2.5 

51 

52 
53 
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57 
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9.66  946 
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9.67  018 
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24 
24 
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9.72  293 

9-72323 
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9.72  384 
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30 
31 
30 
31 
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31 
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3O 

0.27  707 
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0.27  646 
0.27  616 
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9-94  "54 
9.94  647 
9.94  640 

9.94  634 
9-94  627 
9.94  620 

9.94614 
9-94  607 
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7 
7 
6 

7 
7 
6 

7 

7 

7 

9 

8 

7 
6 
5 
4 
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2 
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2 

3 

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6 
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6.4   7.8   7.5 
10.7  12.9  12-5 

15.0  18.1  17.5 
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27.9  —  — 

60 

9.67  161 

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0.27  433 

9-94  593 

O 

L.  Cos, 

d. 

L,  Cot, 

c,  d 

L,  Tan, 

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d. 

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P.P. 

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9-72  598 
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0.27  402 
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0.26  795 
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9-73  687 
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30 
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4  3.2  2.8 

5  4-o  3-5 

6  4.8  4.2 

7  5-6  4-9 
8  6.4  5.6 
9  7«2  6.3 

40 

9.70  761 

21 

9-77  303 

2Q 

O.22  697 

9-93457 

2O 

41 
42 

9.70  782 
9.70803 

21 
21 

9-77  332 
9.77361 

29 
29 

0.22  668 
O.22  639 

9-93  45° 
9-93  442 

8 

7 

19 

18 

43 
44 

45 
46 

% 

49 

9.7°  824 
9.70  846 
9.70  867 
9.70  888 
9.70  909 
9.70931 
9.70952 

22 
21 
21 
21 
22 
21 
21 

9-77  39° 
9.77418 

9-77  447 
9.77476 

9-77  5°5 
9-77  533 
9-77  562 

28, 
29 
29 
29 
28 

29 
2Q 

O.22  582 
0-22553 
O.22  524 
0.22495 
0.22467 
O.22  438 

9-93  435 
9-93427 
9-93  420 
9.93412 

9-93  405 
9-93  397 
9-93  390 

8 

8 

7 
8 

8 

I7 
16 

15 
H 

13 

12 
II 

777 
30  29  28 
o 

5O 

9-70973 

21 

9-77  59i 

28 

O.22  409 

9-93  382 

7 

10 

2.1   2.1   2.O 
f\  A   f\  o   f\  r\ 

51 

52 
53 
54 

H 

57 
58 
59 

9.70  994 
9.71015 
9.71  036 
9.71058 
9.71  079 
9.71  loo 

9.71  121 
9.71  142 
9.71  163 

21 
21 
22 
21 
21 
21 
21 
21 
21 

9.77619 
9-77  648 
9.77677 

9-77  7°6 
9-77  734 
9-77  763 

9-77  79i 
9.77  820 
9.77  849 

29 
29 

29 

28 
29 
28 

29 
29 
28 

0.22  381 
O.22  352 
0.22  323 
O.22  294 
O.22  266 
0.22  237 
O.22  209 
O.22  l8o 
,O.22  151 

9-93  375 
9-93  367 
9-93  36o 
9-93  352 
9-93  344 
9.93  337 
9-93  329 
9-93  322 
9-93  3*4 

8 

7 
8 
8 
7 
8 

8 

7 

9 

8 

7 
6 

5 
4 

3 

2 

I 

't  10.7  10.4  10.0 
•>  15.0  14.5  14.0 
4  19.3  1  8.6  1  8.0 

5   23.6  22.8  22.0 
27.9  26.9  26.0 

60 

9.71  184 

9.77877 

O.22  123 

9-93  3°7 

O 

L,  Cos, 

d. 

L,  Cot, 

c,  d. 

L.  Tan, 

L.  Sin, 

d, 

f 

P,  P,        1 

59' 


31° 


451 


f 

L.  Sin. 

d. 

L.  Tan, 

c.  d. 

L.  Cot, 

L.  Cos. 

d. 

p.  p. 

0 

9.71  184 

o  i 

9.77877 

20 

O.22  123 

9-93  3°7 

8 

60 

I 

2 

3 
4 

i 

8 
9 

9.71  205 
9.71  226 

9.71  247 

0.71  289 

9.71  310 

9-7:  33i 
9-7.1  35- 

9-71  373 

21 
21 
21 
21 

21 
21 
21 
21 

9-77933 

9-77963 
9.77992 
9.78020 

9.78049 
9.78077 

9./8  135 

29 
28 

28 
29 
28 

29 
28 

0.22  094 
O.22065 
0.22037 
0.22  008 
0.21  980 
0.21  951 
0.21  923 
O.2I  894 
O.2I  865 

9-93  299 
9.93  291 

9.93  284 

9-93  276 
9.93  269 
9-93  261 
9-93  253 
9-93  246 
9-93  238 

8 

7 
8 

I 

8 

8 
g 

59 
58 
57 
56 
55 
54 

53 

52 
51 

29   28 

i   2.9   2.8 

2    5.8    5.6 

3   8.7   8.4 
4  n.  6  ii.  2 
^  145  H-o 

IO 

9.7i  393 

21 

9.78  163 

2Q 

0.21  837 

9-93  230 

5O 

6  17.4  1  6.8 

ii 

12 
13 
H 

IS 
16 

*7 
18 

19 

0.71  414 
9-/i  435 
9-71  456 
9.71  477 
9.71  498 
9.71  519 

9-71  539 
9.71  560 
9.71  581 

21 
21 
21 
21 
21 
20 
21 
21 
21 

9.78  192 
9.78  220 
9.78  249 
9.78277 
9.78  306 
9-78334 

9-78  363 
9.78391 

9.78419 

28 
29 
28 
29 
28 
29 
28 
28 
°Q 

0.21  808 
O.2I  780 
0.21  75I 
0.21  723 
O.2I  694 

0.21  666 

O.2I  637 
O.2I  609 
O.2I  ^Sl 

9-93  223 
9-932I5 
9-93  207 
9.93  200 
9-93  192 
9-93  '84 
9-93  i/7 
9-93  l69 
9-93  161 

8 
8 

7 
8 
8 

7 
8 
8 

49 
48 

47 
46 
45 
44 

43 
42 
4i 

7  20.3  19.6 
8  23.2  22.4 
9  26.1  25.2 

21    20 

I  1   2.1    2.0 
2    4-2    4.0 

20 

9.71  602 

2O 

9.78448 

28 

0.21  552 

9-93  !54 

g 

40 

3   6-3   6-o 

21 

22 
23 
24 
25 
26 

27 

28 

29 

9.71  622 

9-71  643 
9.71  664 

9.71  685 

9-71  7°5 
9.71  726 

9-71  747 
9.71  767 
9.71  788 

21 
21 
21 
2O 
21 
21 
2O 
21 
21 

9.78476 
9-/8  505 
978533 
9.78562 
9.78  590 
9.78618 
9.78  647 
9-78  675 
9.78  704 

29 
28 
29 
28 
28 
29 
28 
29 
28 

O.2I  524 

0.21  495 

0.21  467 
0.21  438 
O.2I  410 
O.2I  382 

0.21  353 

0.21  325 
O.2I  296 

9-93  M6 
9-93  138 
9-93I31 
9-93  123 
9-93II5 
9-93  IQ8 
9-93  ioo 
9-93  092 
9-93  084 

8 

7 
8 
8 
7 
8 
8 
8 

39 
38 
37 
36 
35 
34 

33 
32 
3i 

4   8.4   8.0 
5  10.5  10.0 

6   12.6   12.0 

7  14.7  14.0 
8  1  6.8  1  6.0 
9  18.9  18.0 

30 

9.71  809 

2O 

9-78/32 

28 

0.21  268 

9-<>3°77 

/ 

8 

30 

8   7 

31 

32 
33 
34 

3 

37 
38 
39 

9.71  829 
9.71  850 
9.71  870 
9.71  891 
9.71911 
9.71  932 
9.71952 

9-71  973 
9.71  994 

21 
2O 
21 
2O 
21 
2O 
21 
21 
2O 

9.78  760 

9-78  789 
9.78817 

9.78  845 
9.78874 
9.78  902 

9.78  930 

9-78  959 

9.7898- 

29 
28 
28 

29 
28 

28 

29 

28 
28 

O.2I  240 
0.21  211 
O.2I  183 
0.21  155 
O.2I  126 
O.2I  098 
0.21  070 
0.21  041 
O.2I  OI3 

9-93  069 
9.93061 

9-93053 
9.93  046 
9-93  038 
9-93  030 
9.93022 
9.93014 
9.93007 

8 
8 

7 
8 
8 
8 
8 

I 

29 
28 
27 
26 
25 
24 
23 

22 
21 

i  0.8  0.7 

2   1.6   1.4 

3  2.4  2.1 

4  3-2  2.8 
5  4-o  3-5 
6  4.8  4.2 

7  5-6  4-9 
8  6.4  5.6 
9  7.2  6.3 

40 

9.72014 

2O 

9.79015 

28 

0.20  985 

9-92  999 

8 

2O 

4i 

42 

9.72034 
9.72055 

21 

9-79  043 
9.79072 

29 

_Q 

0.20957 
O.20  928 

9.92991 
9-92  983 

8 

19 

18 

43 
44 

45 
46 

47 

48 

49 

9.72075 
9.72  096 
9.72  116 
9-72  137 
9-/2  157 
9.72177 
9.72  198 

21 
2O 
21 
20 
2O 
21 
2O 

9.79  100 

9-79  128 
9.79  156 
9-79  i*>5 
9.79213 

9-79  241 
9.79  269 

28 
28 
29 
28 
28 
28 

?8 

O.2O  9OO 
O.2O  872 
0.20  844 
0.2O  815 
0.20  787 

0.20  7=59 

0.20731 

9-92  976 
9.92  968 
9.92  960 
9.92952 
9.92  944 
9.92936 
9.92929 

7 
8 
8 
8 
8 
8 

8 

»7 

16 

J5 
M 

13 

12 
II 

8    8    8 
30   29   28 
0  1.9   1.8   1.8 

5O 

9.72  218 

2O 

9-79  297 

2Q 

O.2O  703 

9.92921 

8 

IO 

2  5-6  5-4  5-2 

o  A   or   8  S 

5i 

52 
53 
54 

H 

57 
58 
59 

9.72  238 
9.72259 
9.72  279 
9.72  299 
9.72320 
9.72  340 
9.72  360 
9.72  381 
9.72401 

21 
20 
2O 
21 
2O 
2O 
21 
2O 
2O 

9-79  326 
9-79354 
9.79  382 

9.79410 
9-79438 
9.79466 

9-79  495 
9-79523 
9-79  551 

28 
28 
28 
28 
28 
29 
28 
28 
28 

O.2O  674 
O.2O  646 

6.20  618 

O.2O  590 
O.20  562 

0.20  534 

0.20  505 

0.20477 

0.20  449 

9.92913 
9-92  9°5 
9-92  897 
9.92  889 
9.92881 
9.92  874 
9.92  866 
9.92  858 
9  92  850 

8 
8 
8 
8 

7 
8 
8 
8 

8 

9 

8 

7 
6 
5 
4 

3 

2 

I 

3  13.1   12.7   12.2 

?  16.9  16.3  15.8 

5  20.6  19.9  19.2 

24.4  23.6  22.8 

7  28.1  27.2  26.2 

6O 

"72421 

9-79579 

0.20421 

9.92  842 

o 

L.  Cos. 

d. 

L.  Cot. 

c.  d. 

L.  Tan. 

L.  Sin. 

d. 

/ 

p.  p. 

58° 


452 


32' 


1 

L.Sln, 

d, 

L,  Tan,    c,  d. 

L,  Cot, 

L,  Cos, 

d,           |             P,  P, 

o 

9.72421 

20 

9-79579 

?8 

0.20421 

9.92  842 

8 

6O 

I 

9.72441 

9-79  607 

-78 

0.20  393 

9.92  834 

8 

S9 

2 

9.72461 

9-79  635 

28 

0.20  365 

9.92  826 

8 

58 

3 

9.72482 

9-79  663 

oo 

0.20  337 

9.92818 

c 

57 

u 

4 

9.72  502 

9-79  691 

"?& 

O.2O  309 

9.92  810 

56 

29      28      27 

5 

9.72522 

20 

9.79719 

28 

O.2O  28l 

9.92  803 

8 

55 

i 

2.9     2.8     2.7 

6 

9.72  542 

9-79  747 

0.20  253 

9-92  793 

Q 

54 

2 

5.8     5.6     5.4 

8 

9.72562 
9.72  582 

20 

9-79  776 
9.79  804 

29 

28 

0Q 

0.20  224 
O.2O  196 

9.92  787 
9.92  779 

8 
8 

53 
52 

3 
4 

8.7     8.4     8.1 
ii.  6  ii.  2  10.8 

9 

9.72  602 

20 

9-79  832 

28 

0.20  168 

9.92  771 

8 

14.5   14.0  13.5 

IO 

9.72  622 

21 

9.79  860 

28 

O.2O  140 

9.92  763 

8 

50 

20  7  19  6  189 

ii 

12 
13 

9.72  643 
9.72  663 
9.72  683 

2O 
2O 

9.79  888 
9.79916 
9-79  944 

28 
28 
28 

0.20  112 
O.20O84 
O.2OO56 

9-92  753 
9.92  747 
9-92  739 

8 
8 
8 

49 
48 
47 

8 
9 

23.2  22.4  21.6 
26.1  25.2  24.3 

14 

9.72  703 

9-79  972 

~0 

O.2OO28 

9.92  731 

46 

»5 

9-72  723 

9.80000 

~Q 

o.  20  ooo 

9.92  723 

45 

16 

9-72  743 

9.80028 

_o 

0.19972 

9.92715 

44 

17 
18 

9-72  763 
9.72783 

2O 

9.80056 
9.80  084 

25 
28 
08 

0.19944 

0.19  916 

9.92  707 
9.92  699 

8 

43 

42 

i 

21     20     19 

2.1       2.O       1.9 

1  '9 

9.72  803 

2O 

9.80  112 

28 

0.19888 

9.92691 

8 

2 

4.2      4.0      3.8 

20 

9.72  823 

2O 

9.80  140 

28 

0.19  860 

9.92  683 

8 

4O 

3 

6.3     6.0     5.7 

1   21 

9-72  843 

9.80  1  68 

0.19832 

9.92675 

SQ 

4 

8-4     8.0     7.6 

22 
23 

9.72863 
9-72  883 

20 

9.80  195 
9.80  223 

2V 
28 

0.19  805 

0.19777 

9.92  667 
9.92659 

8 

38 

37 

6 

10.5  10.0    9.5 

12.6    I2.O    II.4 

24 

25 
26 

9.72  902 
9.72922 
9.72  942 

19 
20 
2O 

9.80  251 
9.80  279 
9.80  307 

2o 

28 
28 
28 

0.19  749 
0.19  721 
0.19693 

9.92651 
9.92  643 
9-92  635 

»  00  OO  O 

36 
35 
34 

8 
9 

14.7  14.0  13.3 
16.8  16.0  15.2 
18.9  18.0  17.1 

27 

9.72962 

9-8o  335 

•?8 

0.19665 

9.92627 

33 

28 

9.72982 

9.80  363 

_o 

0.19637 

9.92  619 

^2 

29 

9.73002 

2O 

9.80391 

28 

0.19  609 

9.92  611 

8 

30 

9.73022 

9.80419 

28 

0.19  581 

9-92  603 

Q 

30 

987 

31 

32 

9.73041 
9.73061 

20 

9.80  447 
9.80  474 

27 

0-19553 
0.19526 

9-92  593 
9.92  587 

8 

29 

28 

i 

2 

0.9    0.8    0.7 
1.8    1.6    1.4 

33 

9.73081 

9.80  502 

28 

0.19498 

9-92  579 

8 

27 

s 

2-7     2.4     2.1 

34 

9.73  101 

9.80  530 

«Q 

0.19  470 

9.92571 

Q 

26 

4 

3.6    3.2    2.8 

35 

9-73  121 

9-8o  558 

?8 

0.19442 

9-92  563      o 

25 

5 

4-5    4-0    3-5 

36 

9.73  140 

19 

9.80  586 

_0 

0.19  414 

9-92  553 

24 

6 

5.4    4.8    4.2 

38 

9-73  1  60 
9.73  1  80 

20 
20 

9.80  614 
9.80  642 

28 

0.19  386 
0.19358 

9.92546      |        o 

9-92  538  1    * 

23 

22 

8 

6.3    5.6    4.9 
7.2    6.4    5.6 

39 

9-73  200 

9.80  669 

28 

0.19331 

9-92  530 

8 

21 

9 

8.1    7.2    6.3 

4O 

9.73219 

9.80  697 

28 

0.19303 

9.92  522 

8 

20 

41 

9-73  239 

9.80  725 

08 

0.19275 

9.92514 

IQ 

42 

9-8o  753 

•?Q 

0.19247 

9.92  506 

18 

Q  71278 

19 

Q    8O    78l 

O  IQ  2IQ 

44 

9-73  298 

20 

9.80   808 

27 

_0 

0.19  192 

9.92  490 

8 

17 
16 

9-73  3'8 

20 

9.80  836 

_o 

O.I9  164 

9.92  482 

15 

46 

9-73  337 

I9 

9.80  864 

28 

O.I9  136 

9-92  473 

9 

14 

47 

9-73  357 

9.80  892 

0.19  108 

9.92  465 

n 

ft         8         7 

48 
49 

9-73377 
9-73  396 

19 

9.80919 

9.80  947 

28 

28 

0.19081 

0.19053 

9.92457 
9.92  449 

8 

12 

ii 

29     28      28 

SO 

9.73416 

IQ 

9.80  975 

28 

0.19025 

9.92441 

8 

10 

T 

1.8     1.8     2.0 

51 

9-73  435 

9.81  003 

0.18997 

9.92433 

9 

2 

5.4     5.2     6.0 

52 
53 
54 
55 

9-73453 
9-73474 

9-73  494 
9-73  5'3 

19 
20 

19 
2O 

9.81  030 
9.81  058 
9.81  086 
9.81  113 

27 

28 
28 
27 

28 

0.18970 
0.18942 
0.18914 
0.18887 

9-92423 
9.92416 

9.92  408 
9.92  400 

9 
8 
8 
8 

8 
7 
6 
5 

3 

4 

9.1     8.8  10.0 
12.7  12.2  14.0 
16.3  15.8  18.0 

19.9    19.2    22.O 
23.6   22.8    26.O 

& 

9-73  533 

9.81  141 

28 

0.18859 

9.92  392 

4 

I 

27.2   26.2     — 

57 

9-73552 

19 

9.81  169 

0.18831 

9.92  384 

3 

8 

58 

9-73572 

9.81  196 

27 

0.18804 

9.92  376 

2 

59 

9-73591 

19 

9.81  224 

28 

0.18  776 

9.92  367 

1 

i 

60 

9.73611 

9.81  252 

0.18748 

9-92  359 

0 

L,  Cos,      d,       L,  Cot,   |c,  d.    L.  Tan,       L,  Sin.       d, 

t 

P,  P, 

57° 


33' 


453 


/ 

L,  Sin, 

d, 

L,  Tan, 

c,  d. 

L,  Cot. 

L,  Cos, 

d. 

p.p. 

0 

9.73611 

IQ 

9.81  252 

27 

o.i  8  748 

9-92  359 

8 

6O 

I 

2 

3 
4 

I 

8 
9 

9-73  63° 
9-73  65° 
9-73  669 
9-73  689 
9-73  7°8 
9-73  727 
9-73  747 
9-73  766 
9-73  785 

2O 
19 
2O 

19 
19 
2O 

19 
19 
2O 

9.81  279 
9.81  307 
9-8i  335 
9.81  362 
9.81  390 
9.81418 
9.81  445 

9-8  1  473 
9.81  500 

28 
28 

27 
28 
28 

27 
28 

27 
28 

0.18  721 
0.18693 
o.i  8  665 
0.18638 
0.18  610 
0.18582 

o-i8555 
0.18  527 
0.18  500 

9.92351 
9-92  343 
9-92  335 
9-92  326 
9.92318 
9.92310 
9.92  302 
9.92  293 
9.92  285 

8 
8 

9 
8 
8 

8 

9 
8 

8 

51 

D8 

57 
56 
55 
54 

53 
52 
51 

28        27 

i      2.8      2.7 

3      84      11 
4    ii.  2     10.8 

5     '4-o     13-5 
6     16  8     16  2 

IO 

9-73  805 

IQ 

9.81  528 

28 

0.18  472 

9.92  277 

8 

50 

7     19.6     18.9 

ii 

12 
13 
J4 

15 

16 

J7 
18 

19 

9-73^4 
9-73  843 
9-73  863 
9-73  882 
9.73901 
9-73921 
9-73  940 
9-73  959 
973978 

19 
2O 

19 

19 
20 

19 
19 
19 
IQ 

9-8i  556 
9.81  583 
9.81  611 
9.81  638 
9.81  666 
9.81  693 
9.81  721 
9.81  748 
9.81  776 

11 

27 
28 
27 
28 

27 
28 
27 

0.18444 
0.18417 
0.18389 
0.18362 
0.18334 
0.18307 
o.i  8  279 
0.18  252 
o.i  8  224 

9.92  269 
9.92  260 
9.92  252 
9.92  244 
9-92  235 
9.92  227 
9.92219 
9.92211 
9.92  202 

9 
8 
8 

9 
8 

8 
8 

9 
8 

49 
48 

47 
46 
45 
44 

43 
42 
4i 

8    22.4    21.6 
9    25.2     24.3 

20      19      18 

i       2.0     1.9     1.8 

2        4.0      3.8      3.6 

2O 

9-73997 

2O 

9.81  803 

28 

0.18  197 

9.92  194 

g 

4O 

3      6.0     5.7     5.4 

21 

22 
23 
24 
25 
26 

27 
28 

29 

9.74017 
9.74036 
9-74055 
9.74  074 
9-74  093 
9.74H3 
9-74  132 
9-74I5I 
9.74  170 

19 
19 

19 

19 
2O 

19 
19 
19 
IQ 

9.81  831 
9.81  858 
9.81  886 
9.81913 
9.81  941 
9.81  968 
9.81  996 
9.82023 
9.82  051 

27 
28 
27 
28 

27 
28 

27 
28 

27 

0.18  169 
0.18  142 
0.18  114 
0.18087 
o.i  8  059 
o.i  8  032 
0.18004 
0.17977 
0.17949 

9.92  186 
9.92  177 
9.92  169 
9.92  161 
9-92  152 
9.92  144 

9.92  136 
9.92  127 
9.92119 

9 
8 

8 

9 
8 

8 

9 
8 
8 

39 
38 
37 
36 
35 
34 

33 
32 
3i 

4      8.0     7.6     7.2 
5     10.0    9.5     9.0 
6     12.0  11.4  10.8 
7     14.0  13.3  12.6 
8     16.0  15.2  14.4 
9     18.0  17.1   16.2 

30 

9.74  189 

IQ 

9.82078 

•*/ 

28 

0.17922 

9.92  in 

30 

9         8 

3i 
32 

33 
34 

11 

37 
38 
39 

9.74208 
9-74  227 
9.74  246 

9-74  265 
9-74  284 
9-74  3°3 
9-74  322 
9-74  34i 
9-74  360 

19 
19 
19 
19 
19 
19 
19 
19 
IQ 

9.82  106 
9.82  133 
9.82  161 
9.82  188 
9.82215 
9.82  243 
9.82  270 
9.82  298 
9.82  325 

27 
28 

27 

27 
28 

27 
28 
27 
27 

0.17894 
0.17867 
0.17839 
0.17812 
0.17785 
0.17757 

0.17  730 
0.17702 
0.17673 

9.92  IO2 
9.92  094 
9.92  086 
9.92077 
9.92  069 
9.92  O6O 
9.92052 
9.92  044 
9-92035 

8 

8 

9 
8 
9 
8 
8 

9 
g 

29 

28 

27 
26 
25 
24 
23 

22 
21 

i    0.9      0.8 
2     1.8       1.6 
3    2.7       2.4 
4    3-6       3-2 
5    4-5      4-0 
6    5.4      4-8 
7    6.3       5.6 
8    7.2      6.4 
9    8.1       7.2 

40 

9-74  379 

IQ 

9.82  352 

•*/ 

28 

o.  1  7  648 

992027 

20 

41 

42 
43 

9-74  398 
9.74417 
9.74  4^6 

19 
19 

9.82  380 
9.82  407 
9.82  435 

27 
28 

0.17620 

0.17593 
o.  17  z6z 

9.92018 

9.92  oio 

9.92  OO2 

8 
8 

19 
18 

17 

44 

45 
46 

47 
48 

49 

9-74  455 
9-74474 
9-74  493 
9-74  512 
9-74531 
9-74  549 

19 
19 
19 
19 
19 
18 

IQ 

9.82462 
9.82  489 
9.82517 
9.82  544 
9.82571 
9-82  599 

27 

27 
28 

27 

27 
28 

0.17538 

0.17  5*11 
0.17483 

0.17456 
0.17429 
0.17  401 

9-9i  993 
9.91  985 
9.91  976 
9.91  968 
9.91  959 
9.91951 

9 
8 
9 
8 

9 

8 

16 
15 
«4 
*3 

12 
II 

998 
28      27      27 

0      1.6     1.5     1.7 

50 

9-74  568 

9.82  626 

^7 

0.17374 

9.91  942 

Q 

IO 

2      4i    4'5     I'1 

5i 

52 
53 
54 
55 
56 

3 

59 

9-74  |87 

9.74  OOD 

9-74  62-5 

9-74  644 
9.74662 
9.74681 

9-74  7°° 
9.74719 

9-74  737 

iy 
19 
19 
19 
18 
19 
19 
19 
18 

IQ 

9.82  653 
9.82681 
9.82  708 

9-82  735 
9.82  762 
9.82  790 
9.82817 
9.82  844 
9.82  871 

27 
28 
27 
27 

27 
28 

27 
27 

3 

0-17347 
0.17319 
0.17  292 
0.17  263 
0.17238 

0.17  210 
0.17  183 
O.I7  156 
O.I7  129 

9-91  934 
9.91  925 
9.91  917 
9.91  908 
9.91  900 
9.91  891 
9.91  883 
9.91  874 
9.91  866 

1 

9 
8 
9 
8 

9 
8 

Q 

9 
8 

7 
6 
5 
4 

3 

2 

7.8     7.5     8.4 
J     10.9  10.5  1  1.  8 
4     14.0  13.5   15.2 
5     17.1   16.5  18.6 

2O.2    19.5    21.9 

7    23.3  22.5  25.3 

9      26.4    25.5      — 

60 

9-74  756 

9.82  899 

0.17  101 

9-91  857 

O 

L,  Cos. 

d. 

L,  Cot. 

c,  d. 

L.  Tan. 

L,  Sin. 

d. 

/ 

P.P. 

56' 


454 


34' 


1 

L.  Sin. 

d, 

L,  Tan. 

c.  d. 

L.  Cot. 

L,  Cos. 

d. 

p.  p. 

o 

9-74756 

IQ 

9.82  899 

27 

0.17  101 

9.91  857 

8 

60 

I 

2 

3 

4 

i 

8 
9 

9-74  775 
9-74  794 
9.74812 

9.74831 
9.74  850 
9.74  868 
9.74887 
9.74  906 
9-74  924 

19 

18 
19 

19 

18 

19 
19 

18 

IQ 

9.82  926 
9-82  953 
9.82  980 

9.83  008 

9.83035 
9.83  062 

9.83  089 
9.83117 
9.83  144 

27 

27 
28 

27 
27 
27 
28 
27 
27 

0.17074 
0.17047 
0.17  020 
0.16  992 
0.16  965 
0.16938 
0.16  911 
0.16883 
0.16856 

9.91  849 
9.91  840 
9.91  832 
9.91  823 
9.91  815 
9.91  806 
9.91  798 
9.91  789 
9.91  781 

9 

8 

9 
8 
9 
8 

9 

8 

59 

58 
57 
56 
55 
54 
53 
S2 
51 

28   27   26 

i   2.8  2.7  2.6 

2    5.6   5.4   5.2 

3   8.4  8.1  7.8 
4  1  1.  2  10.8  10.4 
5  J4-o  13-5  i3-° 

IO 

9-74  943 

18 

9-83  I71 

27 

o.i  6  829 

9.91  772 

50 

6  16.8  16.2  15.6 

ii 

12 

*3 
H 
15 
16 

;i 

19 

9.74961 
9-74  980 
9-74  999 
9.75017 
9.75  036 
9-75  °54 

9-75  °73 
9.75091 
9.75  no 

19 
J9 
18 

19 
18 

19 
18 

19 
18 

9.83  198 
9-83  225 
9.83  252 

9.83  280 
9-83  307 
9-83  334 
9.83  361 
9.83  388 
9.83415 

27 

27 
28 

27 
27 
27 
27 

27 
27 

0.16802 
0.16775 
o.i  6  748 
o.i  6  720 
o.i  6  693 
0.16666 
o.i  6  639 
0.16  612 
0.16585 

9.91  763 

9-91  755 
9.91  746 

9.91  738 
9.91  729 
9.91  720 
9.91  712 

9.91  703 
9.91  695 

8 
9 
8 

9 
9 
8 

9 

8 

49 
48 
47 
46 
45 
44 

43 
42 
41 

7  19.6  18.9  18.2 
8  22.4  21.6  20.8 
9  25.2  24.3  23.4 

19   18 

i   1.9   1.8 

2   3-8   3-6 

20 

9.75  128 

IQ 

9.83  442 

28 

0.16  558 

9.91  686 

4O 

3   5-7   54 

21 

22 
23 
24 

25 
26 

27 
28 

29 

9-75  H7 
9-75  165 
9.75  184 
9.75  202 
9-75  221 
9-75  239 

9-75  258 
9.75  276 

9-75  294 

18 
19 

18 

19 
18 

19 
18 
18 

IQ 

9-83  47° 
9-83  497 
9-83  524 

9-83551 
9.83  578 
9.83  605 
9.83  632 

9-83  659 
9.83  686 

27 

27 

27 
27 
27 
27 
27 

27 
27 

0.16530 
o.i  6  503 
0.16476 
0.16449 
0.16422 
0.16395 
0.16368 
0.16  341 
0.16  314 

9.91  677 
9.91  669 
9.91  660 
9.91  651 
9.91  643 
9.91  634 
9.91  625 
9.91  617 
9.91  608 

8 
9 
9 
8 
9 
9 
8 
9 

39 
38 
37 
36 
35 
34 

33 
32 
31 

4   7.6   7.2 

5   9-5   9-° 
6  11.4  10.8 
7  13.3  12.6 
8  15.2  14.4 
9  17.1  16.2 

3O 

9.75313 

18 

9-83  7J3 

27 

0.16  287 

9-9i  599 

g 

3O 

9   8 

3i 

32 
33 

34 

35 
36 

38 
39 

9-75  33i 
9-75  35o 
9-75  368 
9-75  386 
9-75  405 
9-75  423 
9-75  44i 
9-75  459 
9-75  478 

19 
18 

18 

19 

18 

18 
18 

19 
18 

9-83  740 
9-83  768 
9-83  795 
9.83  822 
9.83  849 
9.83  876 

9-83  903 
9-83  930 
9.83957 

28 

27 
27 

27 

27 
27 

27 
27 
27 

o.i  6  260 
0.16  232 
o.i  6  205 
0.16  178 
o.i  6  151 
o.i  6  124 
o.i  6  097 
0.16070 
0.16043 

9.91  591 
9.91  582 
9-91  573 

9-91  565 
9-91556 
9-91  547 

9-91  538 
9.91  530 
9.91  521 

9 
9 
8 

9 
9 
9 
8 
9 

29 

28 
27 
26 
25 
24 
23 

22 
21 

i  0.9  0.8 
2  1.8  1.6 

3  2.7  2.4 
4  3-6  3-2 
5  4-5  4-0 
6  5-4  4-8 
7  6.3  5.6 
8  7.2  6.4 
9  8.1  7.2 

4O 

9-75  496 

18 

9.83  984 

27 

0.16016 

9.91  512 

8 

20 

41 
42 

9-75  5H 
9-75  533 

19 

T  S 

9.84011 
9.84  038 

27 

0.15989 
0.15  962 

9.91  504 
9-91  495 

9 

19 
18 

43 

44 
45 
46 

47 

48 
49 

9-75551 
9-75  569 
9-75  587 
9-75  605 
9.75  624 

9-75  642 
9.75  660 

lo 

18 
18 
18 

19 
18 
18 
18 

9.84  065 
9.84092 
9.84119 
9.84  146 
9.84173 
9.84  200 
9.84  227 

27 
27 

27 
27 

27 
27 

27 
27 

0.15935 
0.15  908 
0.15  881 
0.15  854 
0.15  827 
0.15  800 
o-'S  773 

9.91  486 
9.91  477 
9.91  469 
9.91  460 

9-91  451 
9.91  442 

9.9i  433 

9 
9 
8 
9 
9 
9 

1 

17 
16 

15 

H 

13 

12 
II 

988 
28   28   27 

0   1.6  1.8  1.7 

50 

9-75  678 

18 

9.84  254 

26 

0.15  746 

9.91  425 

10 

2   4-7  5-2  5-i 

5i 

52 
53 
54 
55 
56 

H 

59 

9-75  696 
9-75  7J4 
9.75  733 
9-75  751 
9-75  769 
9-75  787 
9-75  805 
9-75  823 
9-75  841 

18 
19 
18 
18 
18 
18 
18 
18 
18 

9.84  280 
9.84  307 
9-84  334 
9.84361 
9.84  388 
9.84415 

9.84  442 
9.84469 
9.84  496 

27 
27 
27 
27 

27 
27 

27 
27 
27 

0.15  720 
0.15693 
0.15  666 
0.15  639 
0.15  612 
0.15585 

O.I5558 
o.i553i 
0.15  504 

9.91  416 
9.9:  407 
9.91  398 
9.91  389 
9.91  381 
9.91  372 

9-91  363 
9.9i  354 
9-91  345 

9 
9 
9 
8 
9 
9 
9 
9 

1 

7 
6 

5 
4 

3 

2 
I 

7.8  8.8  8.4 

3   IO.9  12.2  II.  8 

4  14.0  15.8  15.2 
I  17.1  19.2  18.6 

20.2  22.8  21.9 

7  23.3  26.2  25.3 
9  *4  - 

6O 

9-75  859 

9-84  523 

°-I5477 

9-91  336 

0 

L.  Cos, 

d, 

L,  Cot, 

|c,  d 

L,  Tan, 

L,  Sin, 

d. 

t 

P,  P, 

55' 


35' 


455 


/ 

L.  Sin. 

d. 

L.  Tan. 

c,  d. 

L.  Cot. 

L.  Cos. 

d. 

P.  P. 

0 

9-75  859 

18 

9*4523 

27 

^•15  477 

9.9i  336 

8 

60 

I 

2 

3 

4 

6 

I 

9 

9-75877 
9-75  895 
9-759I3 
9-75931 
9-75  949 
9-75  967 

9-75  985 
9.76003 
9.76021 

18 

18 
18 
18 
18 
18 
18 
18 
18 

9.84  550 
9.84576 
9-84  603 
9.84  630 
9.84  657 
9.84  684 
9.84711 
9.84  738 
9.84  764 

26 
27 
27 
27 
27 
27 

27 
26 
27 

0.15450 
0.15424 
0-15397 
0.15370 

0.15  343 
0.15  316 

0.15  289 
0.15  262 
0.15  236 

9.91  328 

9-91  3i9 
9.91  310 

9.91  301 
9.91  292 
9.91  283 
9.91  274 
9.91  266 
9.91  257 

9 
9 
9 
9 
9 
9 
8 
9 

59 
58 
57 
56 
55 
54 

53 
52 
5^ 

2 

3 

4 

8 

27   26 

2.7   2.6 

5-4   5-2 
8.1   7.8 
10.8  10.4 

13-5  i3-o 
16.2  15.6 
18.9  18.2 

21.6   20.8 

10 

9.76039 

18 

9.84  791 

•/ 

27 

0.15  209 

9.91  248 

5O 

9 

24.3  23.4 

ii 

12 
13 
14 

II 

!7 

18 
19 

9.76057 
9.76075 
9.76093 
9.76  in 
9.76  129 
9.76  146 
9.76  164 
9.76  182 

9.76  200 

18 
18 
18 
18 
17 
18 
18 
18 
18 

9.84818 
9.84  845 
9.84  872 
9.84  899 
9.84  925 
9.84952 
9.84979 
9.85  006 
9.85  033 

*l 

27 
27 
27 
26 

27 
27 
27 

27 
26 

0.15  182 

0.15  155 
0.15  128 

0.15  101 
0.15075 
0.15  048 
0.15021 
0.14994 
0.14967 

9.91  239 
9.91  230 

9.91  221 
9.91  212 
9.91  203 
9.91  194 
9.91  185 
9.91  176 
9.91  167 

9 

i 

i 

9 

I 

q 

49 

48 
47 
46 
45 
44 

43 

42 

4i 

i 

2 

3 
4 

6 

I 

18   17 

1.8   1.7 
3-6   3-4 
5-4   5-i 
7.2   6.8 
9.0   8.5 

10.8   10.2 

12.6  11.9 
14.4  13.6 

20 

9.76218 

18 

9-85  059 

0.14941 

9.91  158 

40 

9 

16.2  15.3 

21 

22 
23 

24 

11 

27 

28 
29 

9.76  236 
9.76253 
9.76271 

9.76  289 
9.76  307 

9-76  324 
9.76  342 
9.76360 
9.76  378 

!i 

18 
18 

!7 

18 
18 
18 

I  7 

9.85  086 
9.85113 
9.85  140 
9.85  166 

9-85  193 
9.85  220 

9.85  247 

9-85  273 
9.85  300 

*/ 

27 
27 

20 

27 
27 
27 
26 

27 

07 

0.14914 

0.14887 
0.14860 
0.14834 
0.14807 
0.14  780 

0.14753 
0.14727 
0.14  700 

9.91  149 
9.91  141 
9.91  I32 
9.91  123 
9.91  114 
9.91  105 
9.91  096 
9.91  087 
9.91  078 

8 
9 
9 
9 
9 
9 
9 
9 

3| 
3° 
37 
36 
35 
34 

33 
32 
31 

2 

3 

4 

7 

10   9   8 

i.o  0.9  0.8 
2.0  1.8  1.6 
3.0  2.7  2.4 
4.0  3.6  3.2 
5.0  4.5  4.0 
6.0  5.4  4.8 
7.0  6.3  5.6 

30 

9-76  395 

18 

9.85  327 

0.14  673 

9.91  069 

30 

8 

8.0  7.2  6.4 

3i 

32 

9-76413 
9-7643I 

18 
17 

9-85  354 
9-85  38o 

26 
27 

0.14  646 
0.14  620 

9.91  060 
9.91051 

9 
9 

29 
28 

9 

9.0  8.1  7.2 

33 
34 

35 
36 

37 
38 
39 

9.76  448 
9.76466 
9.76  484 
9.76  501 
9.76519 

9-76537 
9-76  554 

18 

18 

'7 
18 
18 

!/ 

18 

9.85  407 

9.85  434 
9.85  460 
9.85  487 

9.85  5H 
9.85  540 

9-85  567 

27 
26 

27 
27 
26 
27 
?7 

O.H593 
0.14  566 
0.14540 
0.14513 
0.14486 
0.14  460 
0.14433 

9.91  042 

9-91  033 
9.91  023 
9.91  014 
9.91  005 
9.90  996 
9.90  987 

9 

10 

9 
9 
9 
9 

2/ 
26 

25 
24 

23 

22 
21 

0 

i 

2 

10   10 
27   26 

1.4   1.3 
4-0   3-9 
68   6s 

40 

9.76572 

18 

9.85  594 

-/ 
26 

0.14406 

9.90  978 

20 

3 

9-4   9-1 

4i 
42 
43 
|  44 
45 
46 

47 
48 
49 

9.76  590 
9.76  607 
9.76625 
9.76  642 
9.76  660 
9.76677 
9.76  695 
9.76712 
9.76  730 

!1 

'7 
18 

17 
18 

\l 

I  7 

9.85  620 

9-85  647 
9.85  674 

9.85  700 
9-85  727 
9-85  754 
9.85  780 
9.85  807 
9.85  834 

27 

27 

20 

27 
27 
26 

27 
27 
2(> 

0.14  380 

o.i4353 
0.14326 

0.14  300 
0.14273 
0.14  246 
0.14  220 
0.14  193 
0.14  1  66 

9.90  969 
9.90  960 
9.90951 
9.90  942 

9.90  933 
9.90  924 

9.90913 
9.90  906 
9.90  896 

9 
9 
9 
9 
9 
9 
9 
10 

19 
18 

17 
16 
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14 
13 

12 
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4 
6 

8 
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12.2  11.7 
14.8  14.3 
17.6  16.9 

20.2   19.5 
23.0   22.1 
25.6   24.7 

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9.76  747 

1  / 

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9.85  860 

27 

0.14  140 

9.90  887 

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27   26 

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53 
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55 
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9.76  765 
9.76782 
9.76  800 
9.76817 
9-76835 
9.76852 
9.76870 
9.76887 
9.76  904 

17 

18 

17 

18 

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18 

'7 
17 

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9.85  887 

9.85913 
9.85  940 

9.85  967 

9-85  993 
9.86  020 

9.86  046 
9.86073 
9.86  100 

26 
27 
27 
26 

27 
26 
27 
27 

26 

0.14113 
0.14087 
0.14060 
0.14033 
0.14007 
0.13  980 
0.13954 
0.13927 
0.13  900 

9.90  878 
9.90  869 
9.90  860 
9.90851 
9.90  842 
9.90832 
9.90  823 
9.90814 
9-9°  805 

9 
1  9 
9 
9 
10 
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9 

9 
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9 

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7 
6 
5 
4 

3 

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2 

3 
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1.5   1.4 

4-5   4-3 
7-5   7-2 
10.5  10.  i 

13-5  l3-° 
16.5  15.9 
19.5  1  8.8 
I  22.5  21.7 
25.5  24.6 

6O 

9.76922 

9.86  126 

0.13874 

9.90  796 

0 

L.  Cos. 

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L.  Cot. 

c.  d. 

L,  Tan. 

L.  Sin. 

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54' 


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9.76  922 

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9.86  126 

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0.13874 

9.90  796 

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8 
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9-76  939 
9-76957 
9.76974 

9.76991 
9.77  009 
9.77026 

9-77  °43 
9.77061 
9.77078 

18 
J7 
17 
18 

17 
17 

18 

17 

17 

9.86  153 
9.86179 
9.86  206 
9.86  232 
9.86  259 
9.86  285 
9.86312 
9-86  338 
9.86  365 

26 
27 
26 
27 
26 

27 
26 

27 
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0.13847 
0.13  821 
0.13  794 
0.13  768 
0.13  741 
o-i37i5 
0.13688 
0.13  662 
0-1363? 

9.90  787 
9.90  777 
9.90  768 

9.90  759 
9.90  750 
9.90  741 
9.90  731 
9.90  722 
9.90  713 

IO 

9 

9 
9 
9 

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9 
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59 

58 
57 
56 
55 
54 
53 
52 
51 

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2 

3 
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27   26 

2.7   2.6 

5-4   S-2 
8.1   7.8 
10.8  10.4 
13-5  13-0 

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9-77  °95 

1  7 

9.86  392 

26 

o.  1  3  608 

9.90  704 

IO 

5O 

6 

16.2  15.6 

ii 

12 
13 

14 
15 

16 

II 

19 

9.77  112 
9.77  130 
9-77  M7 
9-77  J64 
9-77  181 
9.77  199 

9.77216 
9-77  233 
9-77  250 

18 
'7 
17 
17 
18 

17 
J7 
J7 
18 

9.86418 
9-86  445 
9.86471 

9.86  498 
9.86  524 
9-86551 
9.86577 
9.86  603 
9.86  630 

27 
26 

27 
26 
27 
26 
26 

3 

0.13582 

0-13555 
0.13529 

0.13  502 
0.13476 
0.13449 
0.13423 

0-13397 
0.13370 

9.90  694 
9.90  685 
9.90  676 
9.90  667 
9.90657 
9.90  648 

9-90  639 
9.90  630 
9.90  620 

9 
9 
9 

IO 

9 
9 

9 

10 

49 

48 

47 
46 

45 
44 

43 
42 

4i 

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9 

2 

18.9  18.2 

21.6   20.8 

24.3  23.4 

18  17   16 

t.8  1.7  1.6 

3-6  3-4  3-2 

20 

9.77  268 

17 

9.86  656 

27 

0.13  344 

9.90  611 

4O 

3 

5.4  5-i  4-8 

21 

22 
23 
24 

25 
26 

27 
28 
29 

9.77  285 
9-77  302 
9-773I9 
9-77  336 
9-77353 
9-77  37° 
9-77  387 
9-77  405 
9.77422 

n 

17 
17 
17 
17 
J7 
18 

J7 

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9.86  683 
9.86  709 
9.86  736 
9.86  762 
9.86  789 
9.86815 
9.86  842 
9.86  868 
9.86  894 

*/ 

26 
27 
26 
27 
26 

27 
26 
26 
27 

O.I33I7 
0.13  291 
0.13  264 
0.13  238 
0.13211 
0.13  185 
0.13  158 
0.13132 
0.13  106 

9.90  602 
9.90  592 
9-90  583 

9.90574 
9-90  565 
9.90555 
9.90  546 

9-90  537 
9.90527 

10 

9 
9 
9 

10 

9 
9 

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11 

37 
36 
35 
34 

33 
32 
31 

4 

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8  i, 
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j.2  6.8  6.4 
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D.8  IO.2   9.6 
2.6  Il.g  II.  2 

1-4  13.6  12.8 
3.2  15.3  14.4 

3O 

9-77  439 

I  7 

9.86  921 

26 

0.13079 

9.90518 

3O 

10   9 

31 

32 
33 
34 
35 
36 

37 
38 
39 

9-77  456 
9-77473 
9-77  490 
9-77  5°7 
9-77  524 
9-77  54i 
9-77558 
9-77575 
9-77  592 

17 

J7 
17 

'7 

17 

J7 
J7 
17 

1  7 

9-86  947 
9.86974 
9.87  ooo 
9.87027 

9-87053 
9.87079 

9.87  106 
9.87  132 
9.87  158 

27 
26 

27 
26 
26 
27 
26 
26 
27 

0.13053 
0.13026 
0.13000 
0.12973 
0.12947 

O.I2  921 

O.I  2  894 
0.12868 
O.I  2  842 

9.90  509 
9-90  499 
9.90  490 

9.90  480 
9.90471 
9.90  462 
9.90452 
9.90  443 
9-90  434 

10 

9 

10 

9 
9 

IO 

9 
9 

IO 

29 
28 
27 
26 

25 
24 

23 

22 
21 

i 

2 

3 

4 

I 
I 

9 

i.o  0.9 

2.0   1.8 

3.0  2.7 
4.0  3.6 

5-o  4-5 
6.0  5.4 
7-o  6.3 
8.0  7.2 
9.0  8.1 

4O 

9-77  609 

1  / 
17 

9-87  185 

*t 

26 

O.I28I5 

9.90424 

Q 

20 

4i 

42 

9.77  626 
9-77  643 

17 

9.87  211 
9.87  238 

27 
nf 

O.I  2  789 
0.12  762 

9.90415 
9.90  405 

10 

19 
18 

43 
44 

4£ 
46 

47 
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9.77  660 
9.77677 

9-77  694 
9.77711 

9-77  728 
9-77  744 
9.77761 

J7 
17 
17 
17 

17 
16 

17 

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9.87  264 
9.87  290 
9-873I7 

9-87  343 
9.87  369 
9.87  396 
9.87422 

26 

% 

26 
27 
26 
26 

O.I  2  736 
O.I2  710 
O.I  2  683 
O.I2  657 
O.I  2  631 
O.  I  2  604 
O.I2  578 

9.90  396 
9.90  386 

9-90377 
9.90  368 

9.90358 
9.90  349 
9-90  339 

9 

10 

9 
9 

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9 

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16 
J5 
M 
13 

12 
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0 

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9    9 
27   26 

1.5   1.4 

50 

9-77  778 

1  / 
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9.87  448 

27 

0.12552 

9.90  330 

IO 

IO 

2 

4-5   4-3 

5i 

52 
53 
54 

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59 

9-77  795 
9.77812 

9-77  829 

9-77  846 
9.77  862 
9.77879 
9.77  896 
9-779I3 
9-77  930 

'7 
17 
17 

16 

*7 

17 
"7 

11 

9-87  475 
9.87  501 
9.87527 

9-87  554 
9.87  580 
9.87  606 

9-87  633 
9.87  659 
9.87  685 

26 
26 
27 
26 
26 

27 
26 
26 
26 

0.12525 
0.12499 
0.12473 
O.I  2  446 
O.I  2  420 
0.12394 
O.I2  367 
O.I2  341 
O.I23I5 

9-90  320 
9.90311 
9-90  301 
9.90  292 
9.90  282 
9.90  273 
9.90  263 
9.90  254 
9.90  244 

9 

10 

9 

10 

9 

10 

9 

IO 
Q 

1 

7 
6 
5 
4 

3 

2 

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3 

4 

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9 

7-5   7«z 
10.5  10.1 

13-5  13-° 
16.5  15.9 
19.5  18.8 
22.5  21.7 
25.5  24.6 

60 

9.77  946 

9.87711 

O.I  2  289 

9.90  235 

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1 

L,  Cos, 

d. 

L,  Cot. 

c.  d. 

L.  Tan. 

L.  Sin. 

d. 

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P.  P. 

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L,  Sin, 

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L.  Tan, 

c,  d. 

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d. 

P,  P.      I 

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9-77  946 

17 

9.87711 

27 

^O.I2  289 

9-90  235 

IO 

6O 

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2 

3 
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8 
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9-77  963 
9.77980 

9-77997 
9.78013 
9.78  030 
9.78  047 
9.78063 
9.78080 
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17 

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16 

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9.87  738 
9.87  764 
9.87  790 
9.87817 

9.87  843 
9.87  869 

9.87  895 
9.87  922 
9.87  948 

26 
26 
27 
26 
26 
26 

% 

26 

O.I  2  262 
O.I  2  236 
O.I2  21O 
0.12  183 
O.I2I57 
0.12  131 
0.12  105 
0.12078 
O.I2  052 

9.90  225 
9.90216 
9.90  206 
9.90  197 
9.90  187 
9.90  178 
9.90  1  68 
9.90159 
9.90  149 

9 

10 

9 

10 

9 

10 

9 

10 
IO 

H 

57 
56 
55 
54 

53 
52 
51 

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2 

3 
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27   26 

2.7   2.6 

5-4   5-2 
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10.8  10.4 
13-5  i3-o 

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10 

9-78113 

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9.87  974 

26 

O.I  2  O26 

9.90  139 

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50 

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18  9  18  2 

ii 

12 
13 
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18 

19 

9.78  130 

9-78  H7 
9.78  163 

9.78  180 
9.78  197 
9.78213 
9.78  230 
9.78  246 
9.78  263 

1  / 

17 

16 

17 

17 
16 

«7 

16 

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9.88000 
9.88027 
9.88053 
9.88  079 
9.88  105 
9-88  131 
9.88  158 
9.88  184 

9.88  210 

27 
26 
26 
26 
26 
27 
26 
26 
26 

O.I2OOO 
O.II973 
0.11947 

o.ii  921 
o.i  i  895 

O.II  869 

o.ii  842 
o.ii  816 
o.ii  790 

9.90  130 
9.90  1  20 
9.90  in 
9.90  101 
9.90091 
9.90082 
9.90072 
9.90063 
9.90053 

10 

9 

IO 
10 

9 

10 

9 

10 
IO 

49 
48 
47 
46 
45 
44 

43 
42 
4i 

8 
9 

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2 

21.6   20.8 

24.3  23.4 

17   16 

1.7   1.6 
34   3-2 

20 

9.78  280 

1  / 
16 

9.88  236 

->6 

o.ii  764 

9.90  043 

Q 

40 

3 

5.1   4.8 

21 
22 
23 
24 

3 

27 
28 
29 

9.78  296 

9-783I3 
9.78329 

9.78  346 
9.78  362 
9-78  379 

9-78  395 
9.78412 
9.78428 

17 
16 

17 
16 

17 
16 

17 
16 

9.88  262 
9.88  289 
9.88315 

9-88  341 
9.88  367 
9-88  393 
9.88  420 
9.88  446 
9.88472 

27 
26 

26 
26 
26 
27 
26 
26 
26 

o.ii  738 
o.ii  711 
o.ii  685 
o.ii  659 

0.11633 

o.ii  607 
o.ii  580 
o.ii  554 
o.ii  528 

9.90  034 
9.90  024 
9.90014 
9.90  003 
9-89  995 
9-89  985 
9.89  976 
9.89  966 
9.89  956 

10 
10 

9 

10 
IO 

9 

10 
IO 

39 
38 
37 
36 
35 
34 

33 
32 
3i 

4 

I 
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9 

6.8   6.4 

8.5   8.0 

10.2    9.6 
II.9   1  1.  2 

13.6  12.8 

15.3   14.4 

30 

9-78  445 

I7 
16 

9.88  498 

26 

o.ii  502 

9.89  947 

IO 

3O 

10   9 

3i 

32 
33 

34 
35 

36 

3 

39 

9.78461 
9.78478 
9.78  494 
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9./8527 
9-78  543 
9.78  560 
9.78576 
9.78  592 

J7 
16 

16 

17 

16 

17 
16 

16 

9.88  524 
9.88  550 
9-88  577 
9.88  603 
9.88  629 
9-88  653 
9.88  68  1 
9.88  707 
9-SS  735 

26 

27 
26 
26 
26 
26 
26 
26 
26 

o.ii  476 
o.ii  430 
o.ii  423 
o.ii  397 
o.ii  371 
0.11345 
0.11319 
o.ii  293 
o.ii  267 

9-89  937 
9-89927 
9.89918 

9.89  908 
9.89  898 
9.89  888 
9.89  879 
9.89  869 
9.89  859 

IO 

9 

IO 
IO 
10 

9 

10 
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29 
28 
27 
26 
25 
24 

23 

22 
21 

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2 

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4 

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8 
9 

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2.0   1.8 

3.0  2.7 
4.0  3.6 

5-o  4-5 
6.0  5.4 
7.0  6.3 
8.0  7.2 
9.0  8.1 

4O 

9.78  609 

X7 
16 

9-88  759 

o.ii  241 

9.89  849 

20 

41 

9.78625 

17 

9.88  786 
9  88  812 

z/ 
26 

o.ii  214 

on  1  88 

9.89  840 

Q  80  8lO 

10 

19 

rC 

42 
43 
44 

tl 

47 
48 
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9.78658 

9-78  674 
9.78691 
9.78  707 

9-78723 
9-78  739 
9.78  756 

16 
16 

17 
16 

16 
16 

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9.88  838 
9.88  864 
9.88  890 
9.88916 
9.88  942 
9.88  968 
9.88  994 

26 
26 
26 
26 
26 
26 
26 
26 

o.ii  162 
o.ii  136 

O.I  I  I  IO 

o.  1  1  084 
o.i  i  058 
o.ii  032 
o.ii  006 

9.89  820 
9.89810 
9.89  80  1 
9.89  791 
9.89  78l 
9.89  771 
9.89  761 

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10 

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10   10 
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9.78772 

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9.89  020 

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0.10980 

9.89  752 

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6.8   6.5 

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52 
53 
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9.78  788 
9.78  803 
9.78821 

9-78  837 
9-78  853 
9.78869 

9.78  886 
9.78902 
9.78918 

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16 
16 
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16 
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9.89  046 
9.89  073 
9.89  099 
9.89125 
9.89  151 
9.89177 
9.89  203 
9.89  229 
9-89  255 

27 
26 

26 

26 
26 
26 
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0.10954 

o.io  927 
o.io  901 
o.io  875 
0.10849 
0.10823 

0.10797 

o.io  771 

0.10745 

9.89  742 
9.89  732 
9.89  722 
9.89712 
9.89  702 
9.89  693 

9-89  683 
9.89673 
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9.89  281 

o.io  719 

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9.89  653 

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9.78  950 
9.78  967 
9.78983 
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9.79015 
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9-79  047 
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9.89  307 
9-89  333 
9-89  359 
9.89  385 
9.89411 
9-89437 
9.89  463 
9.89489 
9-89  51  5 

26 

26 
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o.io  693 
o.io  667 
o.io  641 
0.10615 
o.io  589 
0.10563 

0.10537 

o.io  511 
0.10485 

9.89  643 

9-89  633 
9.89  624 

9.89  614 
9.89  604 
9.89  594 

9-89  584 
9-89  574 
9.89  564 

IO 

9 

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10 
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59 

58 
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53 
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26   25 

2.6   2.5 
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10.4  10.0 
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9-79  095 

16 

9.89541 

26 

0.10459 

9-89  554 

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50 

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18.2  17.5 

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12 
13 
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J7 
18 

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9.79111 
9.79  128 
9.79  144 
9.79  1  60 
9-79  176 
9-79  192 
9.79  208 
9.79  224 
9.79  240 

17 
16 

16 
16 
16 
16 
16 
16 
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9-89  567 
9-89  593 
9.89  619 

9-89  645 
9.89671 

9-89  697 
9.89  723 
9.89  749 
9.89  775 

26 
26 
26 
26 
26 
26 
26 
26 
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0.10433 

0.10407 
0.10381 

0-10355 

0.10329 
o.io  303 
0.10277 
o.io  251 

O.IO  22^ 

9.89  544 

9-89  534 
9.89  524 

9.89514 
9.89  504 
9.89  495 
9.89485 

9.89475 
9.89465 

10 
IO 
IO 
IO 

9 

10 
IO 
10 
IO 

49 
48 

47 
46 

45 
44 

43 
42 
41 

8 

9 

I 

2 

2O.8   2O.O 
23-4   22.5 

17   16   15 

1.7  1.6  1.5 
3-4  3-2  3-o 

20 

9.79  256 

16 

9.89  80  1 

26 

o.io  199 

9-89  455 

IO 

40 

3 

.1  4.5  4.5 
68  64  60 

21 
22 
23 
24 

25 
26 

27 
28 
29 

9-79  272 
9.79  288 
9-79  3°4 
9.79319 
9-79335 
9-79  35  * 
9-79  367 
9-79  383 
9-79  399 

16 
16 

15 

16 
16 
16 
16 
16 
16 

9.89  827 
9.89  853 
9-89  879 
9.89  905 
9.89931 
9.89957 
9.89  983 
9.90  009 
9-90  035 

26 
26 
26 
26 
26 
26 
26 
26 
26 

0.10173 

o.io  147 

O.IO  121 

0.10095 
0.10069 
0.10043 
0.10017 
0.09  991 
0.09  965 

9-89  445 
9-89  435 
9.89425 

9.89415 
9.89  405 
9-89  395 
9-89  385 
9-89  375 
9.89  364 

10 
IO 
IO 
10 
IO 
10 
10 

II 

IO 

39 
38 
37 
36 
35 
34 

33 
32 
31 

6 

8 
9 

8.5  8.0  7.5 

IO.2   9.6   9.O 
II.9  II.  2  10.5 
13.6  12.8  12.0 
15.3  14.4  13.5 

11  10  9 

3O 

9-794I5 

16 

9.90061 

2C 

0.09  939 

9-89  354 

IO 

3O 

3i 
32 
33 
34 
35 
36 

i 

39 

9-79  431 
9-79447 
9-79  463 
9.79478 

9-79  494 
9.79510 

9-79  526 
9-79  542 
9-79  SS8 

16 
16 

15 
16 

16 
16 
16 

16 

I  e 

9.90  086 

9.90  1  1  2 
9.90  138 
9.90  164 
9.90  190 

9.90  216 

9.90  242 

9.90  268 

9.90  294 

•*;> 

26 
26 
26 
26 
26 
26 
26 
26 
26 

0.09  914 
0.09  888 
0.09  862 
0.09  836 
0.09  810 
0.09  784 
0.09  758 
0.09  732 
0.09  706 

9-89  344 
9-89  334 
9.89  324 

9.89314 
9.89  304 
9.89  294 
9.89  284 
9.89  274 
•9.89  264 

IO 
10 
IO 
10 
IO 
10 
IO 
IO 
IO 

29 
28 

27 
26 
25 
24 

23 

22 
21 

i 

2 

3 
4 

6 

8 
9 

i.i  i.o  0.9 

2.2  2.0  1.8 

3-3  3-o  2.7 
4.4  4.0  3.6 

5-5  5-°  4-5 
6.6  6.0  5.4 

7-7  7-°  6.3 
8.8  8.0  7.2 
9.9  9.0  8.1 

4O 

9-79573 

•j 

16 

9.90  320 

26 

0.09  680 

9.89  254 

2O 

4i 
42 

9-79  589 
9-79  605 

16 

9.90  346 
9.90371 

25 

0.09  654 
0.09  629 

9.89  244 
9  89  233 

II 

19 

18 

43 
44 
45 
46 

47 
48 
49 

9.79621 

9-79  636 
9.79  652 
9.79  668 
9-79  684 
9-79  699 
9-79  7'5 

ID 

15 

16 
16 
16 

II 

16 

9-90  397 
9.90423 
9.90  449 
9-90  475 
9.90  501 
9.90527 
9-90553 

26 
26 
26 
26 
26 
26 
26 

0.09  603 
0.09  577 
0.09551 
0.09  525 
0.09  499 
0.09  473 
0.09  447 

9.89  223 
9.89213 
9.89  203 
9.89  193 

9-89  183 
9.89  173 
9.89  162 

IO 
10 
IO 
10 
IO 
IO 

II 

IO 

*7 

16 
15 
H 

J3 

12 
I  I 

o 

10   10   9 
26   25   26 

1.3   1.2   1.4 

50 

9-79  73i 

9.90578 

*j 

26 

0.09422 

9.89  152 

IO 

2 

3-9  3-8  4-3 
6  c  62  72 

5i 

52 
53 
54 

1 

58 
59 

9.79  746 
9-79  762 
9-79  778 

9-79  793 
9-79  809 
9-79  825 
9-79  840 
9-79  856 
9.79872 

*i 

16 
16 

15 
16 
16 

15 
16 
16 

I  e 

9.90  604 
9.90  630 
9.90  656 
9.90  682 
9.90  708 
9-90  734 

9-90  759 
9.90  785 
9.90811 

26 
26 
26 
26 
26 

25 
26 
26 
26 

0.09  396 
0.09  370 
0.09  344 
0.09  3  1  8 
0.09  292 
0.09  266 
0.09  241 
0.09  213 
0.09  189 

9.89  142 
9.89  132 

9.89  122 
9.89  112 

9.89  101 

9.89091 
9.89081 
9.89071 
9.89  060 

IO 

IO 
IO 

II 

IO 
IO 
10 

II 

9 

8 

7 
6 
5 
4 

3 

2 
I 

3 
4 

6 

8 
9 

IO 

9.1  8.8  10.1 
11.7  11.  2  13.0 
14.3  13.8  15.9 
16.9  16.2  18.8 
19.5  18.8  21.7 

22.1  21.2  24.6 
24-7  23-8  — 

60 

9-79  887 

*3 

9.90  837 

0.09  163 

9.89  050 

O 

L,  Cos. 

d. 

L.  Cot. 

c.  d. 

L.  Tan. 

L.  Sin. 

d. 

t 

P.P. 

39' 


459 


f 

L,  Sin. 

d. 

L.  Tan. 

c.  d. 

L.  Cot. 

L.  Cos. 

d, 

P.P. 

0 

9.79887 

16 

9.90  837 

26 

0.09  163 

9.89  050 

IO 

6O 

2 

3 

4 

I 
I 

9 

9-79  903 
9.79918 

9-79  934 
9-79  95° 
9-79  965 
9.79  981 

9.79  996 
9.80012 
9.80027 

15 

16 

16 

11 

15 
16 

!I 

9.90  863 
9.90  889 
9.90914 
9.90  940 
9.90  966 
9.90  992 
9.91  018 
9.91  043 
9.91  069 

26 

25 
26 
26 
26 
26 

'A 

26 

0.09  137 
0.09  i  i  i 
0.09  086 
0.09  060 
0.09  034 
0.09008 
0.08  982 
0.08  957 
0.08  931 

9.89  040 
9.89  030 
9.89  020 
9.89  009 
9.88  999 
9.88989 
9.88  978 
9.88  968 
9.88  958 

IO 
IO 

II 

IO 
IO 

1  1 

10 
10 
IO 

59 

58 
57 
56 

55 
54 

53 
S2 
5i 

i 

2 

3 

4 

6 

26   25 

2.6   2.5 
5-2   5-° 
7-8   7-5 
10.4  10.0 

13.0  12.5 

I  C  6   ISO 

IO 

9.80  043 

i  c 

9.91  095 

26 

0.08  905 

9.88  948 

1  1 

SO 

7 

1  8.2  17.5 

ii 

12 
13 

14 

11 

17 
18 
19 

9.80  058 
9.80074 
9.80  089 
9.80  105 
9.80  1  20 
9.80  136 
9.80151 
9.80  166 
9.80  182 

1  j 
16 

15 
16 

II 

15 

15 
16 

T  - 

9.91  121 
9.91  147 
9.91  172 
9.91  198 
9.91  224 
9.91  250 
9.91  2/6 
9.91  301 
9.91  327 

26 

25 
26 
26 
26 
26 

25 
26 
26 

0.08  879 
0.08  853 
0.08  828 
0.08  802 
0.08  776 
0.08  750 
0.08  724 
0.08  699 
0.08  673 

9.88937 
9.88927 
9.88917 
9.88  906 
9.88  896 
9.88  886 
9.88  875 
9.88  865 
9.8885? 

IO 

IO 

II 

10 
IO 

II 

IO 
10 
J  I 

49 
48 

47 
46 
45 
44 

43 

42 

4i 

8 
9 

i 

2 

3 

2O.8   2O.O 
23.4   22.5 

16   15 

1.6   1.5 
3-2   3-o 
4-8   4-5 

2O 

9.80  197 

1J 

16 

9-9i  353 

26 

0.08  647 

9.88  844 

IO 

40 

4 

6.4   6.0 

21 
22 
23 

24 
25 
26 

27 
28 
29 

9.80213 
9.80  228 
9.80  244 
9.80  259 
9.80  274 
9.80  290 
9.80  305 
9.80  320 
9.80  336 

15 
16 

J5 

:i 

15 

15 
16 

I  C 

9-91  379 
9.91  404 
9.91  430 
9.91  456 
9.91  482 
9.91  507 

9-9i  533 
9-91  559 
9.91  585 

25 
26 

26 
26 

25 
26 
26 
26 

2C 

0.08  621 
0.08  596 
0.08  570 
0.08  544 
0.08518 
0.08  493 
0.08  467 
0.08441 
0.08415 

9-88  834 
9.88  824 
9.88813 
9.88  803 
9.88  793 
9.88  782 
9.88  772 
9.88  761 
9.88751 

IO 

II 

IO 
10 

II 

10 

II 

IO 
IO 

39 
38 
37 
36 
35 
34 

33 

? 
31 

I 
I 

9 

8.0   7.5 
9.6   9.0 

II.  2   10.5 
12.8   I2.O 
14.4   13.5 

11   10 

30 

9.80351 

o 

9.91  610 

*J 
26 

0.08  390 

9.88  741 

30 

3i 

32 
33 
34 

3 

37 
38 
39 

9.80  366 
9.80  382 
9.80  397 
9.80412 
9.80  428 
9.80  443 
9.80  458 
9.80  473 
9.80  489 

I5 

16 

15 
'5 
16 

15 
i5 

11 

I  c 

9.91  636 
9.91  662 
9.91  688 

9-91  7J3 
9-91  739 
9.91  765 

9.91  791 
9.91  816 
9.91  842 

26 
26 

25 
26 

26 
26 

25 

20 

0.08  364 
0.08  338 
0.08  3  1  2 
0.08  187 
0.08  261 
0.08  235 
0.08  209 
0.08  184 
0.08  158 

9.88  730 
9.88  720 
9.88  709 
9.88  699 
9.88  688 
9.88  678 
9.88  668 
9.88  657 
9.88  647 

IO 

II 

10 

II 

IO 
10 

II 

10 
J  I 

29 
28 

27 
26 
25 
24 

23 

22 
21 

3 
4 

6 

8 
9 

3-3  3-o 

4-4  4-0 

5-5  5-o 
6.6  6.0 

7-7  7-° 
8.8  8.0 

9-9  9-0 

40 

9.80  504 

15 

9.91  868 

2C. 

0.08  132 

9.88  636 

IO 

20 

4i 

42 

43 
44 
45 
46 

47 

48 

49 

9.80519 
9.80  534 
9.80  550 
9.80  565 
9.80  580 
9-8o  595 
9.80610 
9.80  625 
9.80  641 

!i 
15 
15 
15 
15 
15 

16 

i  - 

9.91  893 
9.91  919 
9-9  i  945 
9.91971 
9.91  996 
9.92  022 
9.92  048 
9.92  073 
9.92  099 

26 
26 
26 

25 
26 

26 

11 

26 

0.08  107 
0.08081 
0.08055 
0.08  029 
0.08  004 
0.07  978 
0.07  952 
0.07  927 
0.07  901 

9.88  626 
9.88615 
9.88  605 

9.88  594 
9.88  584 
9-88  573 
9.88  563 
9.88  552 
9.88  542 

II 

IO 

II 

IO 

II 

10 

1  1 

10 
I  I 

19 
18 

J7 
16 

15 
H 
13 

12 
II 

0 

i 

2 

11   11 
26   25 

1.2    I.I 

3-5   3-4 
5-9   5-7 

50 

9.80656 

•3 

i  r 

9.92125 

T  - 

9.88531 

IO 

10 

3 

8.3   8.0 

5» 

52 
53 
54 

55 
56 

p 

59 

9.80671 
9.80  686 
9.80  701 
9.80716 
9.80731 
9.80  746 
9.80  762 
9.80  777 
9.80  792 

H 

«5 

'5 
15 
15 

16 

15 
15 

1C 

9.92  150 

9.92  176 

9.92  202 
9.92  227 

9.92  253 
9.92  279 
9.92  304 

9-92  33° 
9.92  356 

*J 

20 
26 

-  5 
26 
26 

-5 
26 
26 

2C. 

0.07  824 
0.07  798 
0.07  773 
0.07  747 
0.07  721 
0.07  696 
0.07  670 
0.07  644 

9.88521 
9.88510 
9.88  499 
9.88  489 
9.88478 
9.88  468 
9.88457 
9.88  447 
9.88430 

II 
II 

10 

II 

10 

1  1 

IO 

II 

1  J 

9 
8 

7 
6 

5 
4 

3 

2 

6 

I 

9 

IO 

ii 

10.6   10.2 

13.0  12.5 
iv4  14-8 
17.7  17.0 

20.1   19.3 

22.5  21.6 

24.8  23.9 

60 

9.80807 

9.92  381 

•*3 

0.07  619 

9.88425 

O 

L.  Cos. 

d.  . 

L.  Cot. 

c.  d. 

L.  Tan. 

L.  Sin. 

d. 

t 

p.  p. 

50' 


460 


40' 


/ 

L.  Sin. 

d. 

L.  Tan. 

c.  d. 

L.  Cot. 

L.  Cos. 

d. 

P.  P. 

0 

9.80807 

I  e 

9.92  381 

?6 

0.07  619 

9-88  425 

10 

60 

I 

2 

3 

4 

I 

9 

9.80  822 
9-80837 
9.80  852 
9.80  867 
9.80  882 
9.80897 
9.80912 
9.80  927 
9.80  942 

15 

'5 
15 
15 
15 
15 
1S 
15 

T  r 

9.92  407 

9-92  433 
9.92  458 

9.92  484 
9.92510 
9-92  535 
9.92561 
9.92  587 
9.92  612 

26 

25 
26 
26 

25 
26 
26 

3 

0.07  593 
0.07  567 
0.07  542 
0.07  516 
0.07  490 
0.07  465 
0.07  439 
0.07413 
0.07  388 

9.88415 
9.88  404 
9-88  394 
9-88  383 
9-88  372 
9.88  362 

9.88351 
9-88  340 
9-88  330 

ii 

10 

II 
II 

IO 

II 
II 

IO 
1  1 

59 
58 
57 
56 
55 
54 

53 
52 
51 

2 

3 

4 

6 

26   25 

2.6   2.5 
5-2   5-o 
7-8   7-5 
10.4  10.0 
13.0  12.5 
15.6  15.0 

10 

9.80957 

T  C 

9.92  638 

21 

0.07  362 

9-88319 

J  J 

50 

7 
g 

15.2   17.5 

ii 

12 
13 
H 

15 

16 

11 

19 

9.80  972 
9.80987 

9.8l  002 
9.8l  017 
9.8l  032 
9.8l  047 

9.81  061 
9.81  076 
9.81  091 

LD 
15 
15 
15 
15 

J5 
H 
15 
i5 

T  C 

9.92  663 
9.92  689 
9.92715 
9.92  740 
9.92  766 
9.92  792 
9.92817 
9.92  843 
9.92  868 

*3 

26 
26 

25 
26 
26 

25 
26 

25 
26 

0-07  337 
0.07311 
0.07  285 
0.07  260 
0.07  234 
0.07  208 
0.07  183 
0.07  157 
0.07  132 

9.88  308 
9.88  298 
9.88  287 
9.88  276 
9.88  266 
9-88  253 
9.88  244 
9.88  234 
9.88  223 

10 

II 
II 

IO 

II 
II 

10 

II 

1  1 

49 
48 

47 
46 
45 
44 

43 

42 

4i 

9 
i 

2 

3 

4 

23-4   22.5 

15   14 

1.5   1.4 

3.0   2.8 
4-5   4-2 
6.0   t;.6 

20 

9.81  106 

1J 

I  c 

9.92  894 

26 

0.07  1  06 

9.88212 

J  J 

4O 

5 

7-5   7-° 

21 

22 
23 
24 

3 

2 

29 

9.81  121 

9.81  136 
9.81  151 
9.81  1  66 
9.81  1  80 
9.81  195 

9.8l  210 
9.8l  225 
9.8l  240 

*3 

15 
15 
15 
H 

J5 
i5 
15 
15 
id. 

9.92  920 

9-92  945 
9.92971 

9.92  996 
9-93  °22 
9-93  048 

9-93  °73 
9.93  099 
9.93  124 

3 

25 
26 
26 

25 
26 

25 
26 

0.07  080 
0.07  055 
0.07  029 
0.07  004 
0.06  978 
0.06952 
0.06  927 
0.06  901 
0.06  876 

9.88  201 
9.88  191 

9.88  180 

9.88  169 
9.88  158 
9.88  148 

9-88  137 
9.88  126 
9.88115 

10 

II 
II 
II 

10 

II 
II 
II 

IO 

39 
38 
37 
36 

35 

34 

33 
32 
31 

6 

8 
9 

9.0   8.4 
10.5   9.8 

12.0   II.  2 

13.5  12.6 
11   10 

I.I    I.O 

30 

9.8l  254 

T  C 

9-93  i?o 

2C 

0.06  850 

9.88  105 

J  I 

30 

2 

2.2    2.O 

3i 

32 
33 
34 

3 

37 

38 
39 

9.8l  269 
9.8l  284 
9.8l  299 
9.8l  314 
9.8l  328 

9-8  1  343 
9.81  358 
9.81  372 
9-8i  387 

*3 

15 
15 
15 

H 
15 
15 
H 
15 

I  c 

9-93  175 
9.93  201 
9.93  227 

9-93  252 
9.93  278 

9-93  303 
9-93  329 
9-93  354 
9-93  38o 

•*3 

26 
26 

25 
26 

25 
26 

25 
26 
26 

0.06  825 
0.06  799 
0.06  773 
0.06  748 
0.06  722 
0.06  697 
0.06671 
0.06  646 
0.06  620 

9.88  094 
9.88083 
9.88072 
9.88061 
9.88051 
9.88  040 
9.88  029 
9.88018 
9.88007 

II 
II 
II 

10 

II 
II 
II 
II 

II 

29 
28 

27 
26 

25 
24 

23 

22 
21 

3 

4 

8 
9 

3-3   3-o 

4.4  4.0 

5-5   5-° 
6.6   6.0 
7.7   7.0 
8.8   8.0 
9.9   9.0 

40 

9.81  402 

AJ 

9.93  406 

0.06  594 

9.87  996 

J  I 

2O 

4i 
42 
43 
44 

45 
46 

47 
48 

49 

9.81  417 
9.81  431 
9.81  446 
9.81  461 
9.81  475 
9.81  490 
9.81  505 
9.81  519 
9-8i  534 

15 

H 

*s 

15 

H 
15 
15 
14 
15 

I  e 

9-93431 
9-93457 
9-93  482 

9-93  5°8 
9-93  533 
9-93  559 

9-93  584 
9.93610 

9-93  636 

25 
26 

25 
26 

3 

25 
26 
26 

2C 

0.06  569 
0.06  543 
0.06  518 
0.06  492 
0.06  467 
0.06  441 
0.06416 
0.06  390 
0.06  364 

9.87  985 

9-87975 
9.87  964 

9.87953 
9.87  942 
9.87931 
9.87  920 
9.87  909 
9.87  898 

IO 

II 
II 
II 
II 
II 
II 
II 

I  J 

19 

18 
17 
16 
»5 

H 

13 

12 
II 

0 
2 

11   10   10 
26  26   25 

1.2   1.3   1.2 

3-5  3-9  3-8 
5-9  6.5  6.2 

5O 

9.81  549 

AD 

I  A 

9.93  66  1 

^5 
26 

0.06  339 

9.87  887 

IO 

IO 

4 

8.3  9.1  8.8 

5i 

52 
53 
54 
55 
56 

9 

59 

9.81  563 
9.81  578 
9.81  592 
9.81  607 
9.81  622 
9.81  636 
9.81  651 
9.81  665 
9.81  680 

'5 
H 
'5 
15 
14 
15 
14 
15 

IA 

9-93  687 
9.93712 
9-93  738 
9-93  763 
9-93  789 
9.93814 

9-93  840 
9-93  865 
9-93  891 

25 
26 

25 
26 

25 
26 

25 
26 

2C 

0.06  313 
0.06  288 
0.06  262 
0.06  237 

O.O6  211 

0.06  1  86 
0.06  1  60 
0.06  135 
0.06  109 

9.87  877 
9.87  866 

9.87  85! 
9.87  844 

9.87  833 
9.87822 

9.87811 
9.87  800 
9.87  789 

II 
II 
II 
II 
II 
II 
II 
II 

II 

9 

8 

7 
6 

5 
4 

3 

2 

I 

8 
9 

10 

ii 

13.0  14.3  13.8 
15.4  16.9  16.2 
17.7  19.5  18.8 

2O.  I  22.1  21.2 
22.5  24.7  23.8 
24.8  —   — 

60 

9.81  694 

9.93916 

0.06  084 

9.87  778 

0 

L.  Cos. 

d, 

L.  Cot. 

c.  d. 

L.  Tan. 

L.  Sin. 

d. 

f 

P.P. 

49' 


41e 


461 


/ 

L,  Sin, 

d. 

L,  Tan. 

c.  d. 

L.  Cot. 

L.  Cos. 

d. 

P.  P.      j 

0 

9.81  694 

j  - 

9.93916 

26 

0.06  084 

9.87  778 

1  1 

6O 

I 

2 

3 

4 

1 

8 
9 

9.81  709 
9.81  723 
9-8i  738 
9.81  752 
9.81  767 
9.81  781 
9.81  796 
9.81  810 
9.81  825 

1  3 
'4 
15 
H 
15 
14 
15 
H 
15 

9-93  942 
9-93  967 
9-93  993 
9.94018 
9.94  044 
9.94  069 

9-94095 
9.94  120 
9.94  146 

3 

25 
26 

25 

26 

% 

2C 

0.06  058 
0.06  033 
0.06  007 
0.05  982 
0.05  956 
0.05  931 
0.05  905 
0.05  880 
0.05  854 

9.87  767 
9.87  756 
9-87  745 
9-87  734 
9-87  723 
9.87712 

9-87  701 
9.87  690 
9.87  679 

u 
II 
II 
II 
II 
II 
II 
II 

J  1 

59 
58 
57 
56 
55 
54 

53 
52 
51 

2 

3 

4 

6 

26   25 

2.6   2.5 
5.2   5.0 

7-8   7-5 
10.4  10.0 
13.0  12.5 

15.6  15.0 

IO 

9.81  839 

J4 
I  - 

9.94  171 

^j 
26 

0.05  829 

9.87  668 

1  1 

5O 

7 

18.2  17.5 

ii 

12 
13 
14 

!I 

17 

18 

19 

9.81  854 
9.81  868 
9.81  882 
9.81  897 
9.81  911 
9.81  926 
9.81  940 
9-8i  955 
9.81  969 

*3 
H 
H 
15 
H 
'5 
H 

'5 

M 
id. 

9-94  197 

9.94  222 

9.94  248 

9-94  273 
9-94  299 
9-94  324 
9-94  35° 
9-94  375 
9-94  40i 

25 
26 

25 
26 

25 
26 

25 
26 
2r 

0.05  803 
0.05  778 
0.05  752 
0.05  727 
0.05  701 
0.05  676 
0.05  650 
0.05  625 
0.05  599 

9.87657 
9.87  646 
9-87  635 
9.87  624 
9.87613 
9.87  601 
9.87  590 

9-87  579 
9.87  568 

II 
II 
II 
II 

12 
II 
II 
II 
j  i 

49 

48 

47 
46 
45 
44 

43 
42 
4i 

9 
i 

2 

3 

2O.8   2O.O 

23.4  22.5 

15   14 

1.5   1.4 
3-o   2.8 
4-5   4-2 

2O 

9.81  983 

I  r 

9-94  426 

*J 

->6 

0.05  574 

9-87557 

II 

4O 

4 

6.0   5.6 

21 

22 
23 
24 

11 

27 
28 
29 

9.81  998 

9.82  OI2 
9.82026 
9.82  041 
9.82  055 
9.82  069' 

9  82  084 
9.82  098 

9.82  112 

14 

H 
*5 
H 
H 
15 
H 
H 

9.94452 
9-94477 
9-94  5°3 
9-94  528 
9-94  554 
9-94579 
9.94  604 
9-94  630 
9-94  655 

% 

25 
26 

25 
25 
26 

3 

0.05  548 
0.05  523 
0.05  497 
0.05  472 
0.05  446 
0.05  421 
0.05  396 
0.05  370 
0.05  345 

9.87  546 
9-87  535 
9-87  524 

9-87  513 
9.87  501 
9.87  490 

9-87  479 
9.87  468 

9.87457 

II 
II 
II 
12 
II 
II 
II 
II 
1  1 

39 

38 
37 
36 
35 
34 

33 
32 
3i 

6 

8 
9 

7-5   7-0 
9.0   8.4 
10.5   9.8 

12.0   I  1.2 

13.5  12.6 
12   11 

3O 

9.82  126 

i  - 

9.94  68  1 

2C 

005319 

9-87  446 

30 

i 

1.2   I.I 

3i 
32 
33 
34 

3 
3 

39 

9.82  141 
9-82  15^ 
9.82  169 
9.82  184 
9.82  198 
9.82  212 
9.82  226 
9.82  240 
9.82  255 

14 
H 
15 
H 
H 
H 
M 
15 

9.94  706 
9-94  732 
9-94  757 

9-94  783 
9.94  808 

9-94  834 
9-94  859 
9-94  884 
9.94910 

*3 

26 

25 
26 

3 

25 

25 
26 

2C 

0.05  294 
0.05  268 
0.05  243 
0.05  217 
0.05  192 
0.05  1  66 
0.05  141 
0.05  116 
0.05  090 

9-87  434 
9.87423 
9.87412 
9.87  401 
9.87  390 
9.87  378 
9.87  367 
9-87  356 
9-87  345 

II 
II 
II 
II 
12 
II 
II 
II 
1  1 

29 
28 
27 
26 
25 
24 

23 

22 
21 

2 

3 

4 
5 
6 

8 
9 

2.4   2.2 

3-6  3-3 
4-8  4-4 
6.0  5.5 
7.2  6.6 
8.4  7.7 
9.6  8.8 
10.8  9.9 

4O 

9.82  269 

H 

9-94  935 

•*D 

26 

0.05  065 

9-87  334 

12 

20 

1  4i 
42 

43 
44 
45 
46 

47 
48 

49 

9.82  283 
9.82  297 
9.82  311 
9.82  326 
9.82  340 

9.82  354 
9.82  368 
9.82  382 
9.82  396 

H 
H 
15 
H 
H 
H 
M 
H 

14 

9.94961 
9.94  986 
9.95012 

9-95  °37 
9-95  °62 
9-95  088 

9-95  JI3 
9-95  *39 
9-95  l64 

3 

25 

25 
26 

25 
26 

25 
26 

0.05  039 
0.05  014 
0.04  988 
0.04  963 
0.04  938 
0.04912 
0.04  887 
0.04  86  1 
0.04  836 

9.87  322 

9-873" 
9.87  300 

9.87  288 

9-87  277 
9.87  266 

9.87  255 

9-87  243 
9.87  232 

II 
II 
12 
II 
II 
II 
12 
II 
1  1 

!7 

16 
15 
M 

13 

12 
II 

0 

i 

2 

3 

12  12  11 
26  25  25 

I.I   1.0   I.I 

3-2  3-1  3-4 
5-4  S-2  5-7 
7-6  7.3  8.0 

50 

9.82  410 

9-95  !9o 

2C 

0.04  810 

9.87  221 

1  2 

IO 

4 

9.8   9.4  IO.2 

5i 

52 
53 
54 

H 

57 
58 
59 

9.82  424 
9.82439 
9.82453 
9.82467 
9.82481 
9.82  495 
9.82  509 
•9.82  523 
9-82537 

15 

H 
H 
H 
H 
H 
H 
H 

9-95  215 
9.95  240 
9.95  266 
9.95  291 
9-953I7 
9-95  342 
9-95  368 
9-95  393 
9-95  4i8 

25 
26 

25 
26 

25 
26 

25 

M 

0.04  785 
0.04  760 
0.04  734 
0.04  709 
0.04  683 
0.04  658 
0.04  632 
0.04  607 
0.04  582 

9.87  209 
9.87  I98 
9.87  I87 
9.87175 
9.87  164 
9-87  153 
9.87  141 

9.87  130 
9.87  119 

II 
II 
12 
II 
II 
12 
II 
II 
12 

I 

7 
6 
5 
4 
3 

2 
I 

i 

1 

1.9  II-5  12.5 
4.1  13.5  14.8 

6.2  15.6  17.0 

8.4  17.7  19.3 

0.6  19.8  21.6 
2.8  21.9  23.9 
4.9  24.0  - 

6O 

9-82551 

9-95  444 

0.04  556 

9.87  I07 

o 

L,  Cos. 

d. 

L.  Cot. 

c.  d. 

L.  Tan. 

L.  Sin. 

d. 

t 

P.  P. 

48' 


462 


42° 


f 

L,  Sin, 

d, 

L,  Tan, 

c,  d. 

L,  Cot, 

L,  Cos, 

d, 

p.  P, 

o 

9.82551 

14. 

9-95  444 

2C 

0.04  556 

9.87  107 

ii 

6O 

I 

2 

3 
4 

6 
9 

9.82  565 
9.82  579 
9.82  593 
9.82  607 
9.82  621 
9.82  635 
9.82  649 
9.82  663 
9.82  677 

H 
H 

*4 
*4 
H 
H 
H 
H 

14. 

9.95  469 
9-95  495 
9-95  520 

9-95  545 
9-95  571 
9-95  596 
9.95  622 
9-95  647 
9-95  672 

26 

25 
25 
26 

25 
26 

25 
25 
26 

0.04531 
0.04  505 
0.04  480 
0-04  455 
0.04  429 
0.04  404 
0.04  378 
0.04  353 
0.04  328 

9.87  096 
9.87085 
9.87073 
9.87  062 
9.87050 
9.87039 
9.87  028 
9.87  016 
9.87  005 

n 

12 
II 
12 
II 
II 
12 
II 
12 

59 
58 
57 
56 
55 
54 

53 
52 
51 

I 

2 

3 

4 

I 

26   25 

2.6   2.5 
5.2   5.0 
7-8   7-5 
10.4  10.0 
13.0  12.5 
15.6  15.0 

IO 

9.82  691 

9.95  698 

2C 

0.04  302 

9.86993 

1  1 

50 

7 

18.2  17.5 

n 

12 
13 

H 

11 

17 
18 

19 

9.82  705 
9.82719 
9-82  733 
9.82  747 
9.82  761 
9-82  775 
9.82  788 
9.82  802 
9.82816 

X4 
14 

H 
14 

H 
H 
J3 
14 
H 

14. 

9-95  723 
9-95  748 
9-95  774 
9-95  799 
9-95  825 
9-95  850 
9-95  875 
9-95  90i 
9.95  926 

•*J 

3 

25 
26 

25 
25 
26 

3 

0.04  277 
0.04  252 
0.04  226 

0.04  201 
0.04175 
O.O4  150 
O.O4  125 
O.O4  099 
O.O4  074 

9.86  982 
9.86  970 
9.86  959 
9.86947 
9.86  936 
9.86  924 
9.86913 
9.86  902 
9.86  890 

12 
II 
12 
II 
12 
II 
II 
12 
II 

49 
48 

47 
46 
45 
44 

43 

42 

4i 

9 

2 

3 

2O.8   2O.O 
23.4   22.5 

14   13 

1.4   1.3 

2.8    2.6 

4-2   3-9 

C  ft     C  0 

20 

9.82  830 

9-95  952 

O.O4  048 

9.86879 

12 

4O 

4 

5-°   5'2 

7  O    6  C 

21 

22 
23 

24 

3 

27 
28 

29 

9.82  844 
9.82  858 
9.82872 
9.82  885 
9.82  899 
9.82913 
9.82927 
-9.82941 
9-82955 

14 
14 
13 
14 
14 
H 

H 

H 

9-95977 
9.96  002 
9.96028 
9-96053 
9.96078 
9.96  104 
9.96  129 
9-96  155 
9.96  1  80 

25 

§ 

25 

25 
26 

25 
26 

25 

O.O4  O23 
0.03  998 
0.03  972 

0.03  947 
0.03  922 
0.03  896 
0.03  871 
0.03  845 
0.03  820 

9.86  867 
9.86855 
9.86  844 
9.86  832 
9.86  821 
9.86  809 
9.86  798 
9.86  786 
9.86775 

12 
II 

II 
12 
II 
12 
II 
12 

39 
38 
37 
36 
35 
34 

33 
32 
31 

6 

I 

9 

8.4   7.8 
9.8   9.1 

1  1.  2   10.4 

12.6  11.7 
12   11 

1.2    I.I 

3O 

9.82  968 

1  6 

I  A 

9.96  205 

25 
26 

0.03  795 

9-86  763 

II 

3O 

2 

2.4    2.2 

31 

32 
33 

34 

35 
36 

37 
38 
39 

9.82  982 
9.82  996 
9.83010 
9.83023 
9-83  037 
9.83051 

9.83  063 
9.83  078 
9.83  092 

H 

H 
13 
H 
14 

H 
13 
H 

14 

9.96  231 
9.96  256 
9.96  281 
9.96307 
9-96  332 
9.96357 

9-96  383 
9.96  408 

9-96433 

25 
25 
26 

25 
25 
26 

25 
25 
26 

0.03  769 
0.03  744 
0.03  719 
0.03  693 
0.03  668 
0.03  643 
0.03  617 
0.03  592 
0.03  567 

9-86  752 
9.86  740 
9.86  728 
9.86717 
9.86  705 
9.86  694 
9.86  682 
9.86  670 
9.86  659 

I  2 
12 
II 
12 
II 
12 
12 
II 
12 

29 

28 
27 
26 

25 
24 

23 

22 
21 

3 
4 

6 

8 
9 

3-6   3-3 

4.8   4-4 
6.0   5.5 
7.2   6.6 

8-4   7-7 
9.6   8.8 
10.8   9.9 

4O 

9.83  106 

9-96  459 

2C 

0.03  541 

9.86  647 

I  2 

20 

4i 
42 
43 
44 

4! 
46 

47 
48 

49 

9.83  120 

9-83  133 
9.83  147 

9.83  161 
9.83174 
9.83  1  88 
9.83  202 

9-83215 
•9.83  229 

13 
H 
H 
!3 

14 
14 
13 
14 

9.96  484 
9.96510 
9-96  535 
9.96  560 
9.96  586 
9.96611 
9.96  636 
9.96  662 
9.96  687 

^J 
26 

25 
25 
26 

25 
25 
26 

25 

0.03  516 
0.03  490 
0.03  465 
0.03  440 
0.03414 
0.03  389 
0.03  364 
0.03  338 
0.03313 

9-86  635 
9.86  624 
9.86612 
9.86  600 
9-86  589 
9.86577 

9-86  565 
9-86554 
9.86  542 

II 
12 
12 
II 
12 
12 
II 
12 

19 
18 

17 
16 
15 
H 
13 

12 
II 

o 
i 

2 

3 
4 

12  11  11 
26  26  25 

I.I   1.2   I.I 

3-2  3-5  34 
5-4  5-9  5-7 
7.6  8.3  8.0 

50 

9.83  242 

M 

9.96712 

25 
06 

0.03  288 

9-86  530 

10 

5T 

I.O  I^.O  12.  C 

51 

52 
53 
54 
55 
56 

11 

59 

9.83  256 
9.83  270 
9.83  283 
9.83  297 
9.83310 
9-83  324 
9-83  338 
9-83351 
9-83  36? 

14 

!3 

14 
13 

14 
H 
13 
H 

9.96  738 
9.96  763 
9.96  788 
9.96814 
9.96  839 
9.96  864 
9.96  890 
9.96915 
9.96  940 

25 
25 
26 

25 
25 
26 

25 
% 

0.03  262 
0.03  237 

O.O3  212 

0.03  1  86 
0.03  161 
0.03  136 
0.03  no 
0.03  085 
0.03  060 

9.86518 
9.86  507 
9-86  495 
9-86  483 
9.86472 
9.86  460 
9.86  448 
9.86436 
9.86425 

II 
12 
12 
II 
12 
12 
12 
II 

9 

8 

7 
6 
5 
4 

3 

2 
I 

i; 

8i 

% 
\f 

M  15.4  14.8 

3.2  17.7  17.0 

5.4  20.1  19.3 

x6  22.5  21.6 
2.8  24.8  23.9 
1-9  —  — 

60 

9-83  378 

*o 

9.96  966 

0.03  034 

9.86413 

0 

L,  Cos. 

d. 

L,  Cot, 

c,  d. 

L,  Tan, 

L.  Sin, 

d, 

t 

P,  P, 

47° 


43' 


463 


1 

L.  Sin.  |  d. 

L.  Tan.  |c.  d.|  L.  Cot. 

L.  Cos,   d, 

p.  p. 

o 

I 

2 

3 

4 

1 

9 
IO 

ii 

12 
13 

H 

\l 

IS 

19 

20 

21 

22 
23 
24 

25 
26 

3 

29 
30 

31 

32 
33 
34 
35 
36 

37 
38 
39 
4O 

4i 

42 

43 
44 
45 
46 

47 
48 

49 
50 

51 

52 
53 
54 
55 
56 

P 

59 
6O 

9-83  37s 

H 
13 
H 
U 
14 
13 
H 
13 
14 

9.96  966  ; 

-5 

3 

25 

3 

25 
25 
25 
26 

25 

3 

25 

25 
26 

25 
25 
26 
25 
25 
26 

25 
25 

25 
26 

25 
25 
26 

25 
25 
26 
25 
25 

25 
26 

25 

3 

25 

25 
26 
25 
25 

3 

25 

25 

26 

25 
25 

3 

25 

3 

25 
25 

25 
26 

0.03  034 

9.86413  1 

12 
12 
12 
II 
12 
12 
12 
12 
12 
II 
12 
12 
12 
12 
12 
12 
12 
II 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 

13 
12 
12 
12 
12 
12 
12 

13 
12 
12 
12 
12 
12 
13 

60 

59 

58 
57 
56 
55 
54 

53 
52 
51 
50 

49 
48 
47 
46 

45 
44 

43 
42 
4i 
40 

39 
38 
37 
36 
35 
34 

33 
32 
3i 
3O 

29 
28 
27 
26 

25 
24 

23 

22 
21 

2O 

19 

18 
«7 
16 
15 
1.4 
*3 

12 
II 

IO 

9 
8 

7 
6 
5 
4 

3 

2 

O 

2 

3 
4 

i 

8 
9 

i 

2 

3 

4 

I 

9 

2 

3 
4 

6 

8 
9 

28   25 

2.6   2.5 
5-2   5-° 
7-8   7-5 
10.4  10.0 

13.0  12.5 

15.6  15.0 
18.2  17.5 

2O.8   2O.O 

23.4  22.5 

14   13 

1.4   1.3 

2.8    2.6 

4-2   3-9 
5-6   5-2 
7.0   6.5 
8.4   7.8 
9.8   9.1 

II.  2   IO.4 

12.6  11.7 
12  11 

1.2   I.I 
2.4   2.2 

3-6  3-3 
4-8  4-4 

6-°  5-5 
7.2  6.6 

8.4  7-7 
9.6  8.8 
10.8  9.9 

9-83  392 
9.83  405 
9.83419 

9-83  432 
9.83  446 

9-83  459 

9-s3  473 
9.83  486 

9-83  500 
9-835^3 

9.96991 
9.97016 
9.97042 
9.97  067 
9.97  092 
9.97  118 

9-97  H3 
9.97  168 
9.97  193 

0.03  009 

O.O2  984 
0.02  958 

0.02  933 

O.O2  908 
0.02  882 
O.O2  857 
O.O2  832 
0.02  807 

9.86401  ] 
9-86  389 
9.86377 

9.86  366 
9-86  354 
9.86  342 

9.86  330 
9.86318 
9.86  306 

1  j 

9.97  219 

0.02  781 

9.86  295 

9-83  527 
9.83  540 

9-Sj  554 

9-83  567  ; 
9.83  581 

9-83  594 
9.83  608 
9.83621 
9-83  634 
9.83  648 

13 
14 

'3 
H 
13 
'4 

13 
13 
H 
13 
13 
H 
13 
H 

!3 

13 
H 
13 
13 
H 
I3 
13 
U 
H 
13 

'3 
13 
H 
13 
13 
13 
U 
13 
13 
13 
13 
14 
*3 
J3 
13 
U 
13 
U 
H 
13 
'3 
13 
13 
13 

9.97  244 
9.97  269 
9.97  295 
9.97  320 
9-97  345 
9-97  371 

9-97  396 
9.97421 

9-97  447 

O.O2  756 
0.02  731 
0.02  705 
0.02  680 
0.02  655 
O.O2  629 
O.O2  604 

0.02  579 
0.02  553 

9.86  283 
9.86  271 
9.86  259 
9.86  247 
9.86235 
9.86  223 
9.86211 
9.86  200 
9.86  1  88 

9-97  472 

0.02  528 

9.86  176 

9.83  66  1 
9.83  674 
9.83  688 
9.83  701 

9-83  7i3 
9.83  728 

9.83  741 
9-83  755 
9.83  768 

9-97  497 
9-97  523 
9-97  548 

9-97  573 
9-97  598 
9-97  624 
9.97  649 
9.97  674 
9.97  700 

O.O2  503 

0.02  477 

0.02  452 
0.02  427 
O.O2  402 
0.02  376 
O.O2  351 
O.O2  326 
0.02  300 

9.86  164 
9.86  152 
9.86  140 
9.86  128 
9.86116 
9.86  104 
9.86092 
9.86  080 
9.86  068 

9-83  781 

9.97  725 

O.O2  275 

9.86  056 

9-83  795 
9.83  808 
9.83821 

9-83  834 
9.83  848 
9.83  861 
9.83  874 
9.83  887 
9.83901 

9-97  75° 
9-97  776 
9.97  80  1 

9.97  826 
9-97851 
9-97  877 
9.97  902 
9.97  927 
9-97  953 

O.O2  250 
O.O2  224 
0.02  199 

0.02  1  74 

O.O2  149 
O.O2  123 
O.O2  098 
0.02  073 
O.O2  047 

9.86  044 
9.86032 

9.86  020 
9.86  008 
9.85  996 
9.85  984 
9.85  972 
9.85  960 
9.85  948 

9.83914 

9.97  978 

O.O2  O2  2 

9.85  936 

0 

i 

2 

3 
4 

I 

8 
9 

IO 

ii 

12 
13 

13   13   12 
26  25   25 

I.O   I.O   I.O 

3-o  2.9  3.1 
5.0  4.8  5.2 
7.0  6.7  7.3 
9.0  8.7  9.4 
i  i.o  10.6  11.5 
13.0  12.5  13.5 
15.0  14.4  15.6 
17.0  16.3  17.7 
19.0  18.3  19.8 

2  I.O  2O.2  21.9 
23.0  22.1  24.0 
25.0  24.0   

9.83  927 
9.83  940 
9-83  954 
9.83  967 
9.83  980 
9-83  993 
9.84006 
9.84  020 
984033 

9.98  003 
9.98029 
9.98054 
9.98079 
9.98  104 
9.98  130 

9-98  155 
9.98  1  80 
9.98  206 

o.oi  997 
o.oi  971 
o.oi  946 
o.oi  921 
o.oi  896 
o.oi  870 
o.oi  845 
o.oi  820 
o.oi  794 

9.85  924 
9.85912 
9.85  900 

9.85  888 
9.85  876 
9.85  864 
9.85851 
9.85  839 
9.85  827 

9.84  046 

9.98  231 

o.oi  769 

9-85815 

9.84059 
9.84072 
9.84  085 
9.84098 

9.84  112 
9.84  125 
9.84138 
9.84  151 

9.84  164 

9.98  256 
9.98  281 
9.98  307 

9-98  332 
9-98  357 
9.98  383 
9.98  408 

9-98433 
9.98458 

o.oi  744 
o.oi  719 
o.oi  693 
o.oi  668 
o.oi  643 
o.oi  617 
o.oi  592 
o.oi  567 
o.oi  542 

9.85  803 

9-85  79i 

9.85  779 

9-85  766 

9-^5  754 
9.85  742 

9-85  730 
9.85718 
9.85  706 

9.84177 

9.98  484 

o.oi  516 

9.85  693 

L.  Cos.   d, 

L.  Cot.  c.  d.  L.  Tan. 

L.  Sin.  |  d.   '       P.  P, 

461 


464 


44' 


1 

L,  Sin. 

d, 

L,  Tan, 

c,  d, 

L,  Cot, 

L,  Cos, 

d, 

P,  P, 

0 

9.84177 

T7 

9.98484 

2C 

o.oi  516 

9.85  693 

12 

6O 

I 

2 

3 

4 

6 

8 
9 

9.84  190 
9.84  203 
9.84  "2  1  6 
9.84  229 
9.84  242 
9-84  255 
9.84  269 
9.84  282 
9.84  295 

13 
13 

!3 

13 
H 

9.98  509 
9.98  534 
9.98  560 

9.98  585 
9.98  610 
9.98  635 
9.98  661 
9.98  686 
9.98711 

25 
26 

25 
25 
25 
26 

25 
25 
26 

o.oi  491 
o.oi  466 
o.oi  440 
o.oi  415 
o.oi  390 
o.oi  365 
o.oi  339 
o.oi  314 
o.oi  289 

9.85  68  1 
9.85  669 
9-85  657 

9.85  645 
9.85  632 
9.85  620 
9.85  608 
9-85  596 
9-85  583 

12 
12 
12 

J3 
12 

12 
12 

13 
12 

59 

58 
57 
56 
55 
54 
53 

5i 

I 

3 

4  i 
5  i 
6  i 

8,, 

26  25   14 

2.6  2.5  1.4 

5.2  5.0  2.8 

7.8  7.5  4.2 

0.4  10.0  5.6 

3.0  12.5  7.0 

5.6  15.0  8.4 

8.2  17.5  9.8 

IO 

9.84  308 

13 

9-98  737 

2C 

o.oi  263 

9.85  57i 

12 

50 

92 

3  A.  22  C  126 

n 

12 
13 

17 

18 
'  19 

9.84321 
9-84  334 
9-84  347 
9.84  360 
9-84  373 
9.84385 
9.84398 
9.84411 
9.84  424 

13 
13 

13 
12 

13 

9.98  762 
9.98  787 
9.98812 
9.98  838 
9.98  863 
9.98  888 
9.98913 
9.98  939 
9.98  964 

25 
25 
26 

25 
25 

26 

25 
2C 

o.oi  238 
o.oi  213 
o.oi  1  88 
o.oi  162 

o.oi  137 

O.OI  112 

o.oi  087 
o.oi  061 
o.oi  036 

9-85  559 
9.85  547 
9-85  534 
9.85  522 
9.85510 
9-85  497 
9.85  48! 
9-85  473 
9.85  460 

12 

13 
12 
12 

12 
12 

13 
12 

49 

48 

47 
46 

45 
44 

43 

42 

4i 

I 
2 

3 

4 

1 

13   12 

1.3    1.2 

2.6   2.4 
3-9   3-6 

5-2   4-8 
6.5   6.0 
7.8   7.2 

2O 

9-84  437 

I  3 

9.98  989 

26 

o.oi  on 

9.85  448 

12 

40 

7 

9.1   8.4 

21 
22 
23 
24 

9.84  450 
9.84  463 
9.84476 
9.84489 

13 
13 

13 
13 

9.99015 
9-99  040 
9-99  065 
9.99  090 

25 
25 

26 

o.oo  985 
o.oo  960 
o.oo  935 
0.00910 

9-85  436 
9.85  423 
9.85411 

9-85  399 

n  Rr  -7  8  A 

13 
12 

12 
13 

39 
38 
37 
36 

8 
9 

10.4   9.6 
11.7  10.8 

25 
26 

27 
28 
29 

9.84515 
9.84  528 
9.84  540 
9-84  553 

13 
J3 
12 

13 
I  3 

9.99  116 
9.99  141 
9.99  1  66 
9.99  191 
9.99217 

25 
25 
25 
26 

o.oo  859 
o.oo  834 
o.oo  809 
o.oo  783 

9-85  374 
9.85  361 
9-85  349 
9-85  337 

12 

12 

12 

34 
33 

13   13 
26   25 

3O 

9.84  566 

I  3 

9.99  242 

2C 

o.oo  758 

9-85  324 

3O 

o 

I  O    I  O 

32 
33 
34 
35 
36 

3 

39 

9.84  579 
9.84  592 
9.84  605 
9.84618 
9.84  630 
9.84  643 
9.84  656 
9.84  669 
9.84  682 

13 
13 
13 
12 

13 
13 
13 
12 

9-99  267 
9-99  293 
9.99318 

9-99  343 
9.99  368 

9-99  394 
9.99419 

9-99  444 
9.99  469 

*3 

26 

25 

26 
25 
25 
25 
26 

o.oo  733 
o.oo  707 
o.oo  682 
0.00657 
o.oo  632 
o.oo  606 
o.oo  581 
o.oo  556 
o.oo  531 

9.85312 

9-85  299 
9.85  287 

9.85  274 
9.85  262 
9.85  250 
9.85  237 
9.85  225 

9.85  212 

13 
12 

13 
12 
12 

13 
12 
13 

29 
28 

27 
26 

25 
24 

23 

22 
21 

2 

3 

4 

I 
I 

9 

IO 

3.0   2.9 
5.0   4.8 
7.0   6.7  . 
9.0   8.7 
ii.o  10.6 
13.0  12.5 
15.0  14.4 
17.0  16.3 
19.0  18.3 

40 

9.84  694 

9-99  495 

2C 

o.oo  505 

9.85  2OO 

20 

n 

2I.O   2O.2 
23  O   22  I 

41 

42 

43 
44 

4I 
46 

47 
48 
49 

9.84  707 
9.84  720 
9-84  733 

9-84  745 
9.84  758 
9.84  771 

9.84  784 
9.84  796 
9.84809 

13 

12 
13 

12 

13 
13 

9.99  520 
9-99  545 
9-99  57° 
9.99  596 
9.99  621 
9.99  646 

9-99  672 
9.99  697 
9.99  722 

25 

25 
26 

25 
25 
26 

25 
25 

o.oo  480 
o.oo  455 
o.oo  430 
o.oo  404 
o.oo  379 
o.oo  354 
o.oo  328 
o.oo  303 
o.oo  278 

9.85187 

9.85  175 
9.85  162 

9.85  15° 
9.85  137 
9.85  125 

9.85  112 

9.85  100 

9.85  087 

12 

12 

13 
12 

J3 
12 
13 

19 

18 

16 
J5 
H 
13 

12 
II 

12 
13 

0 

2 

25.0   24.0 

12   12 
26   25 

I.I  .   I.O 

3-2   3-1 

5-4   S-2 

5O 

9.84  822 

13 

9-99  747 

26 

o.oo  253 

9.85  074 

IO 

3 

7-6   7-3 

5i 
52 
53 
54 

57 
58 
59 

9-84  835 
9.84  847 
9.84  860 
9.84873 
9.84  885 
9.84  898 
9.84911 
9.84  923 
9.84  936 

12 

13 
12 
13 
13 
12 

13 
13 

9-99  773 
9-99  798 
9.99  823 

9-99  848 
9.99  874 
9.99  899 
9.99  924 
9-99  949 
9-99  975 

25 
25 
25 
26 

25 

25 
26 

o.oo  227 

0.00  202 

o.oo  177 
o.oo  152 
o.oo  126 

0.00  101 

o.oo  076 
o.oo  05  1 
o.oo  025 

9.85  062 

9.85  049 
9.85  037 

9.85  024 
9.85  OI2 

9.84  999 
9.84  986 
9.84  974 
9.84  961 

13 

12 

12 
13 
13 
12 

13 

12 

9 
8 

7 
6 
5 
4 

3 

2 

4 

8 
9 

IO 

n 

12 

9-8   9-4 
11.9  11.5 

14-1  13-5 
16.2  15.6 

18.4  17.7 

20.6  19.8 

22.8   21.9 
24.9   24.0 

60 

9.84  949 

o.ooooo 

o.ooooo 

9.84  949 

0 

L,  Cos, 

d, 

L,  Cot, 

c,  d. 

L,  Tan, 

L.  Sin, 

d, 

1 

P,  P, 

45' 


t 


TABLES    XVII.,    XVIII. 

NATURAL   TRIGONOMETRIC    FUNCTIONS. 


R'M'D  SI*RV.  —  30 


465 


466 


TABLE   XVII.  —  NATURAL  SINES  AN£  COSINES. 

^ 
Natural  Sines.         0  c  \  b 


^ 

Prop. 

Angle. 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

Angle, 

Parts 

for  1', 

0° 

.000000 

.0029  09 

.0058  18 

.0087  27 

.011635 

.0145  44 

.017452 

89° 

2.9 

I 

.017452 

.0203  6 

.0232  7 

.0261  8 

.0290  8 

.03199 

.0349  o 

88 

2.9 

2 

.0349  o 

•0378i 

.0407  i 

.0436  2 

•0465  3 

.0494  3 

•05234 

87 

2.9 

3 

•0523  4 

•05524 

.0581  4 

.0610  5 

•0639  5 

.0668  5 

.0697  6 

86 

2.9 

4 

.0697  6 

.0726  6 

•0755  6 

.0784  6 

.08136 

.0842  6 

.0871  6 

85 

2.9 

5 

.0871  6 

.09005 

.09295 

•0958  5 

.0987  4 

.10164 

'•1045  3 

84 

2-9 

6 

•10453 

.10742 

.11031 

.11320 

.11609 

.11898 

.12187 

83 

2.9 

7 

.12187 

.12476 

.12764 

•13053 

•1334 

•1363 

.1392 

82 

2.9 

8 

.1392 

.142! 

.1449 

.1478 

•1507 

•1536 

.1564 

81 

2.9 

9 

.1564 

•!593 

.1622 

.1650 

.1679 

.1708 

•1736 

80 

2.9 

10 

.1736 

•!765 

.1794 

.1822 

.1851 

.1880 

.1908 

79 

2.9 

ii 

.1908 

•1937 

.1965 

.1994 

.2022 

.2051 

.2079 

78 

2.9 

12 

.2079 

.2108 

.2136 

.2164 

.2193 

.2221 

.2250 

77 

2.8 

13 

.2250 

.2278 

.2306 

•2334 

•2363 

.2391 

.2419 

76 

2.8 

H 

.2419 

.2447 

.2476 

.2504 

•2532 

.2560 

.2588 

75 

2.8 

15 

.2588 

.2616 

.2644 

.2672 

.2700 

.2728 

.2756 

74 

2.8 

16 

.2756 

.2784 

.2812 

.2840 

.2868 

.2896 

.2924 

73 

2.8 

17 

.2924 

.2952 

.2979 

.3007 

•3035 

.3062 

.3090 

72 

2.8 

.18 

.3090 

.3118 

•3H5 

•3173 

.3201 

.3228 

0  .3256 

7i 

2.8 

19 

•3256 

•3283 

•33" 

•3338 

•3365 

•3393 

.3420 

70 

2.7 

20 

.3420 

•3448 

•3475 

•3502 

•3529 

•3557 

.3584 

69 

2.7 

21 

•3584 

.3611 

•3638 

•3665 

.3692 

•37  !  9 

•3746 

68 

2-7 

22 

•3746 

•3773 

.3800 

.3827 

•3854 

.3881 

•3907 

67 

2-7 

23 

•3907 

•3934 

.3961 

.3987 

.4014 

.4041 

.4067 

66 

2.7 

24 

.4067 

.4094 

.4120 

.4147 

•4173 

.4200 

.4226 

65 

2.7 

25 

.4226 

•4253 

.4279 

•4305 

•4331 

•4358 

4384 

64 

2.6 

26 

.4384 

.4410 

•4436 

.4462 

.4488 

45  H 

•4540 

63 

2.6 

27 

4540 

.4566 

4592 

.4617 

•4643 

.4669 

•4695 

62^ 

2.6 

28 

•4695 

.4720 

.4746 

.4772 

•4797 

4823 

.4848 

61 

2.6 

29 

.4848 

.4874 

.4899 

•4924 

•495° 

•4975 

.5000 

60 

2-5 

30 

.5000 

•5025 

•5050 

•5075 

.5100 

•5125 

•SJS0 

59 

2-5 

3i 

•5*50 

•5175 

.5200 

•5225 

•5250 

•5275 

•5299 

58 

2.5 

32 

.5299 

•5324 

•5348 

•5373 

•5398 

.5422 

•5446 

57 

2.5 

33 

•544^ 

•5471 

•5495 

•55i9 

•5544 

.5568 

•5592 

56 

2.4 

34 

•5592 

.5616 

.5640 

.5664 

.5688 

•5712 

•5736 

55 

2.4 

35 

•5736 

.5760 

•5783 

•5807 

•5831 

•5854 

•5878 

54 

2.4 

36 

.5878 

.5901 

•5925 

.5948 

•5972 

•5995 

.6018 

53 

2-3 

37 

.6018 

.6041^; 

.6065 

.6088 

.6111 

.6134 

•6i57 

•  52 

2.3 

38 

•6157 

.6180 

•  .6202 

.6225 

.6248 

.6271 

.6293 

51 

2.3 

'39 

.6293 

.6316 

•6338 

•6361 

•6383 

.6406 

.6428 

50 

2.3 

40 

.6428 

.6450 

.6472 

.6494 

•6517 

•6539 

.6561 

49 

2.2 

4i 

.6561 

.6583 

.6604 

.6626 

.6648 

.6670 

.6691 

48 

2.2 

42 

.6691 

•6713 

•6734 

.6756 

.6777 

.6799 

.6820 

47 

2.2 

43 

.6820 

.6841 

.6862 

.6884 

.6905 

.6926 

.6947 

46 

2.1 

44 

.6947 

.6967 

.6988 

.7009 

.7030 

.7050 

.70^1 

45 

2.1 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

Angle. 

NATURAL  SINES  AND  COSINES  (continued). 
Natural  Sines. 


467 


Prop. 

Angle 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

Angle 

Parts 
for  1'. 

45 

.7071 

.7092 

.7112 

•7133 

.7153 

•7173 

•7!93 

44 

2.0 

46 

•7193 

.7214 

•7234 

•7254 

•7274 

.7294 

.73H 

43 

2.0 

47 

•73'4 

•7333 

•7353 

•7373 

•7392 

•7412 

•7431 

42, 

2.O 

48 

•7431 

•745i 

.7470 

.7490 

•75°9 

1  7528 

•7547 

4i 

•9 

49 

•7547 

.7566 

•7585 

.7604 

.7623 

.7642 

.7660 

40 

•9 

50 

.7660 

.7679 

.7698 

.7716 

•7735 

•7753 

•777U 

39 

•9 

5* 

.7771 

.7790 

.7808 

.7826 

.7844 

.7862 

.7880^ 

38 

.8 

52 

.7880 

•7898 

.7916 

•7934 

•7951 

.7969 

.7986 

37 

.8 

53 

.7986 

.8004, 

.8021 

•8039 

.8056 

.8073 

.8090 

36 

•7 

54 

.8090 

.8107. 

.8124 

.8141 

.8158 

•8i75 

.8192 

35 

•7 

55 

.8192 

.8208 

'.8225 

.8241 

.8258 

.8274 

.8290 

34. 

.6 

56 

.8290 

.8307 

•8323 

•8339 

•8355 

•8371 

•8387 

33 

.6 

57 

.8387 

.8403 

.8418 

.8434 

.8450 

^.8465 

.8480 

32 

.6 

58 

.8480 

.8496 

.8511. 

•8526 

•8542 

•8557 

•8572 

3i 

•5 

59 

.8572 

.8587 

.8601' 

.8616 

.8631 

.8646 

.8660 

3° 

•5 

6O 

.8660 

.8675 

.8689 

.8704 

.8718 

.8732 

.8746 

29 

1.4 

61 

.8746 

.8760 

.8774 

.8788 

.8802 

.8816 

.8829 

28 

1.4 

62 

.8829 

.8843 

.8857 

.8870 

.8884 

•8897 

.8910 

27 

14 

63 

.8910 

•8923 

.8936 

•8949 

.8962 

•8975 

.8988 

26 

•3 

64 

.8988 

.9001 

.9013 

.9026 

.9038 

.9051 

.9063 

25 

•3 

65 

.9063 

•9075 

.9088 

.9100 

.9112 

.9124 

•9135 

24 

.2 

66 

•9  '35 

.9147 

•  -9159 

.9171 

.9182 

.9194 

•9205 

23 

.2 

67 

.9205 

.9216 

.9228 

•9239 

.9250 

.9261 

.9272 

22 

.1 

68 

.9272 

.9283 

•9293 

•9304 

•9315 

•9325 

•9336 

21 

.1 

69 

.9336 

•9346 

•9356 

•9367 

•9377 

•9387 

•9397 

20 

I  JO 

70 

•9397 

•9407,  V 

K  .9417 

.9426 

•9436 

.9446 

•9455 

19 

I.O 

7* 

"•9455 

•9465* 

•9474 

.9483 

.9492 

.9502 

•95  " 

18 

0.9 

72 

•95" 

.9520 

.9528 

•9537 

•9546 

•9555 

•9563 

17 

0.9 

73 

.  -9563 

•9572 

.9580 

.9588 

•9596 

.9605 

.9613 

16 

0.8 

74 

.9613 

.9621 

.9628 

.9636 

.9644 

.9652 

•9659 

15 

0.8 

75 

.9659 

.9667 

.9674 

.9681 

.9689 

..9696 

•97°3 

14 

0.7 

76 

•9703 

.9710 

.9717 

•9724 

•973° 

•9737 

•9744 

13 

0.7 

77 

•9744  • 

•975° 

•9757 

•9763 

.9769 

•9775 

.9781 

12 

0.6 

78 

.9781 

.9787 

•9793 

•9799 

.9805 

.9811 

.9816 

II 

0.6 

79 

.9816 

.9822 

.9827 

•9833 

.9838 

•9843 

.9848 

IO 

o-5 

80 

.9848 

•9853 

.9858 

•9863 

.9868 

.9872 

.9877 

9 

°-5 

81 

.9877 

.9881 

.9886 

.9890 

•9894 

•9899 

•9903 

8 

0.4 

82 

•9903 

.9907 

.9911 

.9914 

.9918 

,.9922 

•9925 

7 

0.4 

83 

.9925 

•9929 

•9932 

•9936 

•9939 

•9942 

•9945 

6 

0.3 

84 

•9945 

.9948 

•995  ' 

•9954 

•9957 

•9959 

.9962 

5 

o-3 

85 

.9962 

.9964 

•9967 

.9969 

.9971 

•9974 

.9976 

4 

O.2 

86 

.9976 

.9978 

.9980 

.9981 

•9983 

•9985 

.9986 

3 

0.2 

87 

.9986 

.9988 

•9989 

.9990 

•9992 

•9993 

•9994 

2 

O.I 

88 

•9994 

•9995 

.9996 

•9997 

•9997 

.9998 

.9998 

I 

O.I 

89 

.9998 

•9999 

•9999 

I.OOOO 

I.OOOO 

I.OOOO 

I.OOOO 

0 

O.O 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

Angle. 

Natural  Cosines. 


468  TABLE   XV11I. —  NATURAL  TANGENTS  AND  COTANGENTS:* 

Natural  Tangents. 


1 

Prop. 

Angle. 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

Angle. 

Parts 

for  1'. 

0° 

.00000 

.0029  i 

.0058  2 

.00873 

.01164 

•0145  5 

.01746 

89° 

2.9 

i 

.01746 

.0203  6 

.0232  8 

.0261  9 

.0291  o 

.0320  i 

.0349  2 

88 

2.9 

2 

.0349  2 

•0378  3 

.0407  5 

f  .0436  6 

.0465  8 

.0494  9 

.0524  I 

.87 

2.9 

3 

.0524  I 

•0553  3 

•0582  4  / 

^06  1  1  6 

.0640  8 

.0670  o 

.0699  3 

^36 

2-9 

4 

.0699  3 

.0728  5  • 

•0757  8 

.0787  o 

.08163 

.084^6 

.0874  9 

85 

2-9 

5 

.0874  9 

.0904  2 

•0933  5 

.09629 

.0992  3 

.1021  6 

.1051  o 

84 

2.9 

6 

.1051  o 

.1080  5 

.11099 

•"394 

.11688 

.11983 

.12278 

83 

2.9 

7 

.12278 

•12574 

.12869 

-wts 

.1346 

•1376 

.1405 

82 

3-o 

8 

.1405 

•1435    ^465 

•1495 

.1524 

•'554 

.1584 

81 

3-o 

9 

.1584 

.1614 

.1644 

•!673 

•1703 

•'733 

•!763 

80 

3-o 

10 

•1763 

•1793 

.1823 

•1853 

.1883 

.1914 

.1944 

79 

3-o 

ii 

.1944 

.1974 

.2004    .2035 

.2065 

•2095 

.2126 

78 

3-o 

12 

.2126 

.2156 

.2186 

.2217 

.2247 

.2278 

.2309 

77 

3-1 

13 

.2309 

•2339 

.2370 

.2401 

•2432 

.2462 

•2493 

76 

3-1 

4 

.2493 

.2524 

•2555 

.2586 

.2617 

.2648 

.2679 

75 

3-i 

15 

.2679 

.2711 

.2742 

•2773 

.2805 

.2836 

.2867 

74 

3-i 

16 

.2867 

.2899 

.2931 

.2962 

•2994 

.3026 

.3057 

73 

3-2 

17 

•3057 

.3089 

.3121 

•3153 

•3185 

•3217 

•3249 

72 

3-2 

18 

•3249 

.3281 

•33H 

•3346 

•3378 

•34" 

•3443 

71 

3-2 

»9 

•3443 

•3476 

.3508 

•3541 

•3574 

.3607 

.3640 

70 

3-3 

20 

.3640 

•3673 

.3706 

•3739 

•3772 

•3805 

•3839 

69 

3-3 

1  2I 

•3839 

.3872 

.3906 

•3939 

•3973 

.4006 

.4040 

68 

3-4 

22 

.4040 

.4074 

.4108 

.4142 

.4176 

.4210 

•4245 

67 

3-4 

23 

4245 

•4279 

•43H 

•4348 

.4383 

.4417 

•4452 

66 

3-5 

24 

•4452 

.4487 

.4522 

4557 

•4592 

.4628 

.4663 

65 

3-5 

25 

.4663 

.4699 

•4734 

.4770 

.4806 

.4841 

.4877 

64 

3-6 

26 

.4877 

4913 

•495° 

.4986 

.5022 

•5059 

•5095 

63 

3-6 

27 

•5°95 

•5!32 

.5169 

.5206 

•5243" 

.5280 

•5317 

62 

3-7 

28 

•5317 

•5354 

•5392 

•5430 

•5467 

•55°5 

•5543 

61 

3-8 

29 

•5543 

.5581 

.5619 

.5658 

.5696 

•5735 

•5774 

60 

3-8 

30 

•5774^ 

.5812 

•5851 

.5890  ' 

•5930 

•5969 

.6009 

59 

3-9 

31 

.6009 

.6048 

.6088 

.6128 

.6168 

.6208 

.6249 

58 

4.0 

32" 

.6249 

.6289 

•6330 

•637  i 

.6412 

•6453 

.6494* 

57. 

4.1 

33 

.6494 

.6536 

•6577 

.6619 

.6661 

.6703 

•6745 

5* 

4.2 

34 

•6745 

.6787 

.6830 

.6873 

.6916 

•6959 

.7002 

55 

4-3 

35 

.7002 

.7046 

.7089 

•7*33 

.7177 

.7221 

.7265 

54 

4-4 

36 

.7265 

•7310 

•7355 

.7400 

•7445 

.7490 

•7536 

53 

4-5 

37 

•7536 

•758i 

.7627 

•7673 

.7720 

.7766 

•7813 

S2 

4.6 

38 

•7813 

.7860 

.7907 

•7954 

.8002 

.8050 

.8098 

51 

4-7 

39 

.8098 

.8146 

•8i95 

.8243 

.8292 

.8342 

.8391 

5° 

4-9 

4O 

.8391 

.8441 

.8491 

.8541 

.8591 

.8642 

.8693 

49 

5-o 

4i 

.8693 

.8744 

.8796 

.8847 

.8899 

.8952 

.9004 

48 

5-2 

42 

.9004 

•9057 

.9110 

.9163 

.9217 

.9271 

•9325 

47 

5-4 

43 

•9325 

.9380 

•9435 

.9490 

•9545 

.9601 

•9657 

46 

5-5 

44 

•9657_ 

•97  *  3 

.9770 

.9827 

.9884 

.9942 

1.  0000 

45 

5-7 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

Angle. 

d 

Natural  Cotangents. 


NATURAL  TANGKXTS  AND  COTANGENTS  (continued). 
Natural  Tangents. 


469 


Prop. 

Angle 

0'      10'     20' 

30'     40' 

50' 

eo' 

Angle 

Parts 

for  V. 

45° 

I.OOOO 

1.0058 

1.0117 

1.0176 

1.0235 

1.0295 

1-0355 

44° 

5-9 

46 

I-°355 

i  .04  1  6 

1.0477 

1.0538 

1.0599 

i.  066  1 

1.0724 

43 

6.1 

47 

1.0724 

1.0786 

1.0850 

1.0913 

1.0977 

1.1041 

1.1106 

42 

6.4 

48 

1.1106 

1.1171 

1.1237 

1.1303 

1.1369 

1.1436 

1.1504 

41 

6.6 

49 

1.1504 

I-I57I 

1.1640 

1.1708 

1.1778 

1.1847 

1.1918 

40 

6.9 

50 

1.1918 

1.1988 

1.2059 

1.2131 

1.2203 

1.2276 

1.2349 

39 

7-2 

51 

1.2349 

1.2423 

,1-2497 

1.2572 

1.2647 

1.2723 

1.2799 

38 

7-5 

52 

1.2799 

1.2876 

1.2954 

1.3032 

1.3111 

1.3190 

1-3270 

37 

7-9 

53 

1.3270 

I-335I 

1.3432 

L3SI4 

'•3597 

1.3680 

J-3764 

36 

8.2 

54 

1.3764 

1.3848 

1-3934 

1.4019 

1.4106 

I-4I93 

1.4281 

35 

8.6 

55 

1.4281 

1.4370 

1.4460 

1-4550 

1.4641 

M733 

1.4826 

34 

9.1 

56 

1.4826 

1.4919 

1-5013 

1.5108 

1.5204 

1.5301 

1-5399 

33 

9.6 

57 

1-5399 

1-5497 

1-5597 

1.5697 

1.5798 

1.5900 

1.6003 

32 

10.  1 

58 

1.6003 

1.6107 

1.6212 

1.6319 

1.6426 

1.6534 

1.6643 

31 

10.7 

59 

1.6643 

'•6753 

1.6864 

1.6977 

1.7090 

1.7205 

1.7321 

30 

"•3 

60 

1.7321 

1-7437 

'•7556 

L7675 

1.7796 

1.7917 

i  .8040 

29 

12.0 

61 

1.8040 

1.8165 

1.8291 

1.8418 

1.8546 

1.8676 

1.8807 

28 

12.8 

62 

1.8807 

1.8940 

1.9074 

1.9210 

1-9347 

1.9486 

1.9626 

27 

13.6 

63 

1.9626 

1.9768 

1.9912 

2.0057 

2.0204 

2-0353 

2.0503 

26 

14.6 

64 

2.0503 

2.0655 

2.0809 

2.0965 

2.1123 

2.1283 

2.1445 

25 

15.7 

65 

2.1445 

2.1609 

2-1775 

2.1943 

2.2113 

2.2286 

2.2460 

24 

16.9 

66 

2.2460 

2.2637 

2.2817 

2.2998 

2.3183 

2.3369 

2-3559 

23 

I8.3 

67 

2-3559 

2.375° 

2.3945 

2.4142 

2.4342 

2-4545 

2-475  J 

22 

19-9 

68 

2-475  1 

2.4960 

2.5172 

2.5386 

2.5605 

2.5826 

2.6051 

21 

21.7 

69 

2.6051 

2.6279 

2.6511 

2.6746 

2.6985 

2.7228 

2-7475 

2O 

23.7 

7O 

2-7475 

2.7725 

2.7980 

2.8239 

2.8502 

2.8770 

2.9042 

19 

71 

2.9042 

2.9319 

2.9600 

2.9887 

3.0178 

3-0475 

3-0777 

18 

72 

3.0777 

3.1084 

3-1397 

3.1716 

3.2041 

3-2371 

3.2709 

17 

73 

3.2709 

3-3052 

3-3402 

3-3759 

3.4124 

3-4495 

34874 

16 

74 

3-4874   3-5261 

3-5656 

3.6059 

3.6470 

3-6891 

3-7321 

'5 

75 

3-7321 

3-776o 

3.8208 

3-8667 

3-9I36 

3-9617 

4.0108 

14 

76 

4.0108   4.0611 

4.1126 

4.1653 

4-2193 

4.2747 

4-33I5 

13 

77 

4.3315  i  4-3897 

4-4494 

4-5107 

4.5736 

4.6382   4.7046 

12 

78 

4.7046   4-7729 

4.8430 

4-9152 

4.9894 

5.0658   5.1446 

II 

79 

5.1446 

5-2257 

5-3093 

5-3955 

54845 

5.5764   5.6713 

IO 

80 

5-67I3 

57694 

5.8708 

5-9758 

6.0844 

6.1970)   6.3138 

9 

81 

6.3138  |  6.4348 

6.5606 

6.6912 

6.8269 

6.9682   7.1154 

8 

82 

7.1154   7.2687 

7.4287 

7-5958 

7.7704 

7.9530   8.1443 

7 

83 

8.1443   8.3450 

8-5555 

8.7769 

9.0098 

9-2553 

9-5J44 

6 

84 

9-5I44 

9.7882 

10.0780 

10.3854 

10.7119 

11.0594 

11.4301 

5 

85 

11.4301   11.8262 

12.2505 

12.7062 

13.1969 

13.7267 

14.3007 

4 

86 

14.3007  114.9244 

15.6048 

16.3499 

17.1693 

18.0750 

19.0811 

3 

87 

19.0811  j  20.2056" 

21.4704 

22.90381-24.5418 

26.4316   28.6363 

2 

88 

28.6363  31.2416 

34-3678 

38.1885  42.9641 

49.1039   57.2900 

I 

89 

57.2900  68.7501 

85.9398 

114.5887  171.8854 

343-7737 

00 

O 

60'     50' 

40' 

30'     20'      10'      0' 

Angle. 

Natural  Cotangents. 


. 


.  4 


V 


'  3^ 


- 


^mO  r^^^y^TT  j  ^T^n^r\ 


YC   13554 


< 


926464 


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